X^2-25x=100

Solution for X^2-25x=100 equation:

X^2-25X=100

We move all terms to the left:

X^2-25X-(100)=0

a = 1; b = -25; c = -100;
Δ = b2-4ac
Δ = -252-4·1·(-100)
Δ = 1025
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:

$\sqrt{\Delta}=\sqrt{1025}=\sqrt{25*41}=\sqrt{25}*\sqrt{41}=5\sqrt{41}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-5\sqrt{41}}{2*1}=\frac{25-5\sqrt{41}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+5\sqrt{41}}{2*1}=\frac{25+5\sqrt{41}}{2}
$