6x^2+2x=12

Solution for 6x^2+2x=12 equation:

6x^2+2x=12

We move all terms to the left:

6x^2+2x-(12)=0

a = 6; b = 2; c = -12;
Δ = b2-4ac
Δ = 22-4·6·(-12)
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{73}}{2*6}=\frac{-2-2\sqrt{73}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{73}}{2*6}=\frac{-2+2\sqrt{73}}{12}
$