4x^2-4x=120

Solution for 4x^2-4x=120 equation:

4x^2-4x=120

We move all terms to the left:

4x^2-4x-(120)=0

a = 4; b = -4; c = -120;
Δ = b2-4ac
Δ = -42-4·4·(-120)
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-44}{2*4}=\frac{-40}{8}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+44}{2*4}=\frac{48}{8}
=6
$