-x^2+20x+75=0

Solution for -x^2+20x+75=0 equation:

-x^2+20x+75=0

We add all the numbers together, and all the variables

-1x^2+20x+75=0

a = -1; b = 20; c = +75;
Δ = b2-4ac
Δ = 202-4·(-1)·75
Δ = 700
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:

$\sqrt{\Delta}=\sqrt{700}=\sqrt{100*7}=\sqrt{100}*\sqrt{7}=10\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-10\sqrt{7}}{2*-1}=\frac{-20-10\sqrt{7}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+10\sqrt{7}}{2*-1}=\frac{-20+10\sqrt{7}}{-2}
$