x*(8-x)=-115

Solution for x*(8-x)=-115 equation:

x(8-x)=-115

We move all terms to the left:

x(8-x)-(-115)=0

We add all the numbers together, and all the variables

x(-1x+8)-(-115)=0

We add all the numbers together, and all the variables

x(-1x+8)+115=0

We multiply parentheses

-1x^2+8x+115=0

a = -1; b = 8; c = +115;
Δ = b2-4ac
Δ = 82-4·(-1)·115
Δ = 524
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{524}=\sqrt{4*131}=\sqrt{4}*\sqrt{131}=2\sqrt{131}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{131}}{2*-1}=\frac{-8-2\sqrt{131}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{131}}{2*-1}=\frac{-8+2\sqrt{131}}{-2}
$