4x^2=52x-120

Solution for 4x^2=52x-120 equation:

4x^2=52x-120

We move all terms to the left:

4x^2-(52x-120)=0

We get rid of parentheses

4x^2-52x+120=0

a = 4; b = -52; c = +120;
Δ = b2-4ac
Δ = -522-4·4·120
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-28}{2*4}=\frac{24}{8}
=3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+28}{2*4}=\frac{80}{8}
=10
$