3x^2-6x=76

Solution for 3x^2-6x=76 equation:

3x^2-6x=76

We move all terms to the left:

3x^2-6x-(76)=0

a = 3; b = -6; c = -76;
Δ = b2-4ac
Δ = -62-4·3·(-76)
Δ = 948
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:

$\sqrt{\Delta}=\sqrt{948}=\sqrt{4*237}=\sqrt{4}*\sqrt{237}=2\sqrt{237}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{237}}{2*3}=\frac{6-2\sqrt{237}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{237}}{2*3}=\frac{6+2\sqrt{237}}{6}
$