12t+9=5t^2
5t^2 -12t -9 = 0
This equation is easily factorable as:
(5t + 3)(t - 3) = 0
So
t = 3 or -3/5
To solve the equation 12t + 9 = 5t^2, we will need to rearrange the equation to get it in a quadratic form, and then solve for t.
Step 1: Move all terms to one side of the equation:
5t^2 - 12t - 9 = 0
Step 2: This equation is now in the form of ax^2 + bx + c = 0, where a = 5, b = -12, and c = -9. To solve for t, we can use the quadratic formula:
t = (-b ± sqrt(b^2 - 4ac)) / (2a)
In this case, a = 5, b = -12, and c = -9:
t = (-(-12) ± sqrt((-12)^2 - 4(5)(-9))) / (2(5))
t = (12 ± sqrt(144 + 180)) / 10
t = (12 ± sqrt(324)) / 10
t = (12 ± 18) / 10
Step 3: Now, we have two possible solutions for t:
t1 = (12 + 18) / 10 = 30 / 10 = 3
t2 = (12 - 18) / 10 = -6 / 10 = -0.6
Therefore, the equation 12t + 9 = 5t^2 has two solutions: t = 3 and t = -0.6.