-x2+8x+75=13

Solution for -x2+8x+75=13 equation:

-x2+8x+75=13

We move all terms to the left:

-x2+8x+75-(13)=0

We add all the numbers together, and all the variables

-1x^2+8x+62=0

a = -1; b = 8; c = +62;
Δ = b2-4ac
Δ = 82-4·(-1)·62
Δ = 312
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:

$\sqrt{\Delta}=\sqrt{312}=\sqrt{4*78}=\sqrt{4}*\sqrt{78}=2\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{78}}{2*-1}=\frac{-8-2\sqrt{78}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{78}}{2*-1}=\frac{-8+2\sqrt{78}}{-2}
$