Final answer:
To solve the quadratic equation 4x²+12x=135, we can use the quadratic formula. The solutions are x = 3 and x = -7.5.
Step-by-step explanation:
To solve the equation 4x²+12x=135, we can first set the equation equal to 0: 4x²+12x-135=0. We can then solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:
x = (-b ± √(b²-4ac)) / 2a
In this equation, a = 4, b = 12, and c = -135. Substituting these values into the quadratic formula, we have:
x = (-12 ± √(12²-4(4)(-135))) / (2(4))
x = (-12 ± √(144+2160)) / 8
x = (-12 ± √2304) / 8
x = (-12 ± 48) / 8
So the solutions to the quadratic equation 4x²+12x=135 are x = (-12 + 48) / 8 = 3 and x = (-12 - 48) / 8 = -7.5.