48x^2-32x=4x+4

Solution for 48x^2-32x=4x+4 equation:

48x^2-32x=4x+4

We move all terms to the left:

48x^2-32x-(4x+4)=0

We get rid of parentheses

48x^2-32x-4x-4=0

We add all the numbers together, and all the variables

48x^2-36x-4=0

a = 48; b = -36; c = -4;
Δ = b2-4ac
Δ = -362-4·48·(-4)
Δ = 2064
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:

$\sqrt{\Delta}=\sqrt{2064}=\sqrt{16*129}=\sqrt{16}*\sqrt{129}=4\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{129}}{2*48}=\frac{36-4\sqrt{129}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{129}}{2*48}=\frac{36+4\sqrt{129}}{96}
$