4x2+48x=288

Solution for 4x2+48x=288 equation:

4x^2+48x=288

We move all terms to the left:

4x^2+48x-(288)=0

a = 4; b = 48; c = -288;
Δ = b2-4ac
Δ = 482-4·4·(-288)
Δ = 6912
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:

$\sqrt{\Delta}=\sqrt{6912}=\sqrt{2304*3}=\sqrt{2304}*\sqrt{3}=48\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-48\sqrt{3}}{2*4}=\frac{-48-48\sqrt{3}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+48\sqrt{3}}{2*4}=\frac{-48+48\sqrt{3}}{8}
$