6x^2=64x+96

Solution for 6x^2=64x+96 equation:

6x^2=64x+96

We move all terms to the left:

6x^2-(64x+96)=0

We get rid of parentheses

6x^2-64x-96=0

a = 6; b = -64; c = -96;
Δ = b2-4ac
Δ = -642-4·6·(-96)
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-80}{2*6}=\frac{-16}{12}
=-1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+80}{2*6}=\frac{144}{12}
=12
$