6x^2-96=60x

Solution for 6x^2-96=60x equation:

6x^2-96=60x

We move all terms to the left:

6x^2-96-(60x)=0

a = 6; b = -60; c = -96;
Δ = b2-4ac
Δ = -602-4·6·(-96)
Δ = 5904
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:

$\sqrt{\Delta}=\sqrt{5904}=\sqrt{144*41}=\sqrt{144}*\sqrt{41}=12\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-12\sqrt{41}}{2*6}=\frac{60-12\sqrt{41}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+12\sqrt{41}}{2*6}=\frac{60+12\sqrt{41}}{12}
$