36x-48=4x^2

Solution for 36x-48=4x^2 equation:

36x-48=4x^2

We move all terms to the left:

36x-48-(4x^2)=0

determiningTheFunctionDomain
-4x^2+36x-48=0

a = -4; b = 36; c = -48;
Δ = b2-4ac
Δ = 362-4·(-4)·(-48)
Δ = 528
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:

$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{33}}{2*-4}=\frac{-36-4\sqrt{33}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{33}}{2*-4}=\frac{-36+4\sqrt{33}}{-8}
$