X^2-48x=-96

Solution for X^2-48x=-96 equation:

X^2-48X=-96

We move all terms to the left:

X^2-48X-(-96)=0

We add all the numbers together, and all the variables

X^2-48X+96=0

a = 1; b = -48; c = +96;
Δ = b2-4ac
Δ = -482-4·1·96
Δ = 1920
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:

$\sqrt{\Delta}=\sqrt{1920}=\sqrt{64*30}=\sqrt{64}*\sqrt{30}=8\sqrt{30}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-8\sqrt{30}}{2*1}=\frac{48-8\sqrt{30}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+8\sqrt{30}}{2*1}=\frac{48+8\sqrt{30}}{2}
$