5x^2-57x=3x-120

Solution for 5x^2-57x=3x-120 equation:

5x^2-57x=3x-120

We move all terms to the left:

5x^2-57x-(3x-120)=0

We get rid of parentheses

5x^2-57x-3x+120=0

We add all the numbers together, and all the variables

5x^2-60x+120=0

a = 5; b = -60; c = +120;
Δ = b2-4ac
Δ = -602-4·5·120
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-20\sqrt{3}}{2*5}=\frac{60-20\sqrt{3}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+20\sqrt{3}}{2*5}=\frac{60+20\sqrt{3}}{10}
$