x^2-20x=25=0

Solution for x^2-20x=25=0 equation:

x^2-20x=25=0

We move all terms to the left:

x^2-20x-(25)=0

a = 1; b = -20; c = -25;
Δ = b2-4ac
Δ = -202-4·1·(-25)
Δ = 500
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:

$\sqrt{\Delta}=\sqrt{500}=\sqrt{100*5}=\sqrt{100}*\sqrt{5}=10\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-10\sqrt{5}}{2*1}=\frac{20-10\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+10\sqrt{5}}{2*1}=\frac{20+10\sqrt{5}}{2}
$