x^2-100x=384

Solution for x^2-100x=384 equation:

x^2-100x=384

We move all terms to the left:

x^2-100x-(384)=0

a = 1; b = -100; c = -384;
Δ = b2-4ac
Δ = -1002-4·1·(-384)
Δ = 11536
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:

$\sqrt{\Delta}=\sqrt{11536}=\sqrt{16*721}=\sqrt{16}*\sqrt{721}=4\sqrt{721}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-4\sqrt{721}}{2*1}=\frac{100-4\sqrt{721}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+4\sqrt{721}}{2*1}=\frac{100+4\sqrt{721}}{2}
$