0=-x^2-16x+75

Solution for 0=-x^2-16x+75 equation:

0=-x^2-16x+75

We move all terms to the left:

0-(-x^2-16x+75)=0

We add all the numbers together, and all the variables

-(-x^2-16x+75)=0

We get rid of parentheses

x^2+16x-75=0

a = 1; b = 16; c = -75;
Δ = b2-4ac
Δ = 162-4·1·(-75)
Δ = 556
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:

$\sqrt{\Delta}=\sqrt{556}=\sqrt{4*139}=\sqrt{4}*\sqrt{139}=2\sqrt{139}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{139}}{2*1}=\frac{-16-2\sqrt{139}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{139}}{2*1}=\frac{-16+2\sqrt{139}}{2}
$