6x^2=60x-144

Solution for 6x^2=60x-144 equation:

6x^2=60x-144

We move all terms to the left:

6x^2-(60x-144)=0

We get rid of parentheses

6x^2-60x+144=0

a = 6; b = -60; c = +144;
Δ = b2-4ac
Δ = -602-4·6·144
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-12}{2*6}=\frac{48}{12}
=4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+12}{2*6}=\frac{72}{12}
=6
$