Can someone please explain how to solve 3x^2+7x-15=0 by using the quadratic equation?
I know that the equation is: ax^2+bx+c=0 but I get confused about how to set the problem up and solve.
Thanks.
Sure! To solve the quadratic equation 3x^2 + 7x - 15 = 0 using the quadratic formula, we first need to identify the values of a, b, and c in the given equation.
In this case:
a = 3
b = 7
c = -15
Now, let's plug these values into the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
Substituting the known values, we get:
x = (-(7) ± √((7)^2 - 4(3)(-15))) / (2(3))
Simplifying this equation gives us:
x = (-7 ± √(49 + 180)) / 6
x = (-7 ± √(229)) / 6
Now, we have two possible solutions:
x = (-7 + √(229)) / 6 (referred to as the positive root)
and
x = (-7 - √(229)) / 6 (referred to as the negative root)
These are the solutions to the given quadratic equation.