86=6x^2-18x

Solution for 86=6x^2-18x equation:

86=6x^2-18x

We move all terms to the left:

86-(6x^2-18x)=0

We get rid of parentheses

-6x^2+18x+86=0

a = -6; b = 18; c = +86;
Δ = b2-4ac
Δ = 182-4·(-6)·86
Δ = 2388
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:

$\sqrt{\Delta}=\sqrt{2388}=\sqrt{4*597}=\sqrt{4}*\sqrt{597}=2\sqrt{597}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{597}}{2*-6}=\frac{-18-2\sqrt{597}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{597}}{2*-6}=\frac{-18+2\sqrt{597}}{-12}
$