4x^2-108=11x

Solution for 4x^2-108=11x equation:

4x^2-108=11x

We move all terms to the left:

4x^2-108-(11x)=0

a = 4; b = -11; c = -108;
Δ = b2-4ac
Δ = -112-4·4·(-108)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-43}{2*4}=\frac{-32}{8}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+43}{2*4}=\frac{54}{8}
=6+3/4
$