6x^2-2x=15

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

6x^2-2x=15

We move all terms to the left:

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}
$