6x^2+2x=78

Solution for 6x^2+2x=78 equation:

6x^2+2x=78

We move all terms to the left:

6x^2+2x-(78)=0

a = 6; b = 2; c = -78;
Δ = b2-4ac
Δ = 22-4·6·(-78)
Δ = 1876
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:

$\sqrt{\Delta}=\sqrt{1876}=\sqrt{4*469}=\sqrt{4}*\sqrt{469}=2\sqrt{469}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{469}}{2*6}=\frac{-2-2\sqrt{469}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{469}}{2*6}=\frac{-2+2\sqrt{469}}{12}
$