x=-5x^2+30x+135

Solution for x=-5x^2+30x+135 equation:

x=-5x^2+30x+135

We move all terms to the left:

x-(-5x^2+30x+135)=0

We get rid of parentheses

5x^2-30x+x-135=0

We add all the numbers together, and all the variables

5x^2-29x-135=0

a = 5; b = -29; c = -135;
Δ = b2-4ac
Δ = -292-4·5·(-135)
Δ = 3541
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-\sqrt{3541}}{2*5}=\frac{29-\sqrt{3541}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+\sqrt{3541}}{2*5}=\frac{29+\sqrt{3541}}{10}
$