X^2-6x=100

Solution for X^2-6x=100 equation:

X^2-6X=100

We move all terms to the left:

X^2-6X-(100)=0

a = 1; b = -6; c = -100;
Δ = b2-4ac
Δ = -62-4·1·(-100)
Δ = 436
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:

$\sqrt{\Delta}=\sqrt{436}=\sqrt{4*109}=\sqrt{4}*\sqrt{109}=2\sqrt{109}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{109}}{2*1}=\frac{6-2\sqrt{109}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{109}}{2*1}=\frac{6+2\sqrt{109}}{2}
$