4x^2-48x=144

Solution for 4x^2-48x=144 equation:

4x^2-48x=144

We move all terms to the left:

4x^2-48x-(144)=0

a = 4; b = -48; c = -144;
Δ = b2-4ac
Δ = -482-4·4·(-144)
Δ = 4608
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:

$\sqrt{\Delta}=\sqrt{4608}=\sqrt{2304*2}=\sqrt{2304}*\sqrt{2}=48\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-48\sqrt{2}}{2*4}=\frac{48-48\sqrt{2}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+48\sqrt{2}}{2*4}=\frac{48+48\sqrt{2}}{8}
$