4x^2-44x=20x+252

Solution for 4x^2-44x=20x+252 equation:

4x^2-44x=20x+252

We move all terms to the left:

4x^2-44x-(20x+252)=0

We get rid of parentheses

4x^2-44x-20x-252=0

We add all the numbers together, and all the variables

4x^2-64x-252=0

a = 4; b = -64; c = -252;
Δ = b2-4ac
Δ = -642-4·4·(-252)
Δ = 8128
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:

$\sqrt{\Delta}=\sqrt{8128}=\sqrt{64*127}=\sqrt{64}*\sqrt{127}=8\sqrt{127}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-8\sqrt{127}}{2*4}=\frac{64-8\sqrt{127}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+8\sqrt{127}}{2*4}=\frac{64+8\sqrt{127}}{8}
$