15=6x^2+2x

Solution for 15=6x^2+2x equation:

15=6x^2+2x

We move all terms to the left:

15-(6x^2+2x)=0

We get rid of parentheses

-6x^2-2x+15=0

a = -6; b = -2; c = +15;
Δ = b2-4ac
Δ = -22-4·(-6)·15
Δ = 364
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:

$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{91}}{2*-6}=\frac{2-2\sqrt{91}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{91}}{2*-6}=\frac{2+2\sqrt{91}}{-12}
$