Final answer:
To solve the equation 3g²-78g=135, we rearrange it into a quadratic equation and use the quadratic formula to find the solutions. The solutions are g = 31.29 and g = -1.145.
Step-by-step explanation:
To solve the equation 3g²-78g=135, we need to rearrange it into a quadratic equation. So let's set it equal to zero: 3g²-78g-135=0. We can then solve this equation by factoring, completing the square, or using the quadratic formula. To keep things simple, let's use the quadratic formula: g = (-b ± √(b²-4ac))/(2a).
For our equation, a = 3, b = -78, and c = -135. Plugging these values into the quadratic formula:
g = (-(-78) ± √((-78)²-4(3)(-135)))/(2(3))
Simplifying further:
g = (78 ± √(6084+1620))/(6)
g = (78 ± √(7704))/(6)
Taking the square root:
g = (78 ± 87.72)/(6)
Final solutions are:
g = (78 + 87.72)/(6) = 31.29
g = (78 - 87.72)/(6) = -1.145