15t^2+7t=2
The quadratic formula tells you that the solutions are:
t = [-b +/-sqrt(b^2 - 4ac]/(2a)
In this case, a = 15, b = 7 and c = -2
See what you get.
In google type:
quadratic equation online
When you see list of results click on:
Free Online Quadratic Equation Solver:Solve by Quadratic Formula
When page be open in rectangle type:
15t^2+7t=2
and click option: solve it
You will see solution step-by step
thank you the site is very helpful.
To solve the equation 15t^2 + 7t = 2, we can use the quadratic formula or factorization method:
Method 1: Quadratic Formula
The quadratic formula states that for an equation in the form of ax^2 + bx + c = 0, the solutions are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, we have a = 15, b = 7, and c = -2. Plugging these values into the quadratic formula:
t = (-7 ± √(7^2 - 4 * 15 * -2)) / (2 * 15)
Calculating the discriminant (D = b^2 - 4ac):
D = 7^2 - 4 * 15 * -2 = 49 + 120 = 169
Since the discriminant is positive (D > 0), we have two real solutions.
t = (-7 ± √169) / 30
t = (-7 ± 13) / 30
From here, we have the two solutions:
t1 = (-7 + 13) / 30 = 6/30 = 1/5
t2 = (-7 - 13) / 30 = -20/30 = -2/3
So, the solutions to the equation are t = 1/5 and t = -2/3.
Method 2: Factorization
To solve the equation by factorization, we want to rewrite it in the form of (kt + m)(pt + n) = 0, where k, m, p, and n are integers.
15t^2 + 7t - 2 = 0
We need to find two numbers that multiply to give -30 (product of the coefficients of t^2 and the constant term) and add up to 7 (coefficient of t).
The numbers are 10 and -3, since 10 * -3 = -30 and 10 + (-3) = 7.
Now we can rewrite the equation:
15t^2 + 10t - 3t - 2 = 0
Factoring by grouping:
5t(3t + 2) - 1(3t + 2) = 0
Now, we can see that we have a common factor:
(3t + 2)(5t - 1) = 0
From here, we set each factor equal to zero:
3t + 2 = 0 or 5t - 1 = 0
Solving each equation, we find:
3t = -2 => t = -2/3
5t = 1 => t = 1/5
So, the solutions to the equation are t = -2/3 and t = 1/5.
Both methods lead to the same solutions: t = 1/5 and t = -2/3.