6x^2=-60x+438

Solution for 6x^2=-60x+438 equation:

6x^2=-60x+438

We move all terms to the left:

6x^2-(-60x+438)=0

We get rid of parentheses

6x^2+60x-438=0

a = 6; b = 60; c = -438;
Δ = b2-4ac
Δ = 602-4·6·(-438)
Δ = 14112
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:

$\sqrt{\Delta}=\sqrt{14112}=\sqrt{7056*2}=\sqrt{7056}*\sqrt{2}=84\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-84\sqrt{2}}{2*6}=\frac{-60-84\sqrt{2}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+84\sqrt{2}}{2*6}=\frac{-60+84\sqrt{2}}{12}
$