(2x+3)/(3x-6) = (5x+3)/(5x - 9)
cross multiply:
(2x+3)*(5x-9) = (3x-6)*(5x+3)
double distribution:
10x^2 - 3x -27 = 15x^2 - 21x - 18
combine like terms:
0 = 5x^2 -18x + 9
Then factor it to find two values of x
(2x+3)*(5x-9)=(3x-6)*(5x+3)
(2x+3)*(5x-9)=(5x+3)*(3x-6)
10x^2+15x-18x-27=15x^2+9x-30x-18
10x^2-3x-27=15x^2-21x-18
0=15x^2-10x^2+3x-21x+3x-18+27
5x^2-18x+9=0
If you want to know that solutions in google type:
quadratic equation online
When you see list of results click on:
webgraphingcom/quadraticequation_quadraticformula.jsp
When page be open in rectacangle type:
5x^2-18x+9=0
and click option solve it
You will see solution step-by-step
To solve this equation, we need to find the value of x that makes both sides of the equation equal. Let's go through the steps to solve it:
Step 1: Simplify the equation
Multiply both sides of the equation by the denominators (3x - 6) and (5x - 9) to eliminate the fractions:
(2x + 3)(5x - 9) = (3x - 6)(5x + 3)
Step 2: Expand the equation
Using the distributive property, multiply each term on the left side by each term on the right side:
10x^2 - 18x + 15x - 27 = 15x^2 - 18x - 30x - 18
Step 3: Combine like terms
Combine like terms on both sides of the equation:
10x^2 - 3x - 27 = 15x^2 - 48x - 18
Step 4: Move all terms to one side of the equation
Rearrange the equation to have all terms on one side, using addition and subtraction:
0 = 15x^2 - 10x^2 - 48x + 3x - 18 + 27
0 = 5x^2 - 45x + 9
Step 5: Solve the quadratic equation
To solve the quadratic equation, we can either factor it or use the quadratic formula. In this case, factoring doesn't seem to be straightforward, so let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 5, b = -45, and c = 9. Substituting these values into the quadratic formula:
x = (45 ± √((-45)^2 - 4 * 5 * 9)) / (2 * 5)
x = (45 ± √(2025 - 180)) / 10
x = (45 ± √(1845)) / 10
Step 6: Simplify the square root
Simplify the square root if possible using a calculator or math software:
x ≈ (45 ± 42.96) / 10
Step 7: Solve for x
Now solve for the two possible values of x by substituting the positive and negative square root solutions:
x1 ≈ (45 + 42.96) / 10 ≈ 8.596
x2 ≈ (45 - 42.96) / 10 ≈ 0.204
Therefore, the solution to the equation is x ≈ 8.596 or x ≈ 0.204.