6x^2=-108x+480

Solution for 6x^2=-108x+480 equation:

6x^2=-108x+480

We move all terms to the left:

6x^2-(-108x+480)=0

We get rid of parentheses

6x^2+108x-480=0

a = 6; b = 108; c = -480;
Δ = b2-4ac
Δ = 1082-4·6·(-480)
Δ = 23184
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:

$\sqrt{\Delta}=\sqrt{23184}=\sqrt{144*161}=\sqrt{144}*\sqrt{161}=12\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-12\sqrt{161}}{2*6}=\frac{-108-12\sqrt{161}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+12\sqrt{161}}{2*6}=\frac{-108+12\sqrt{161}}{12}
$