6x^2-x=18

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

6x^2-x=18

We move all terms to the left:

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

We add all the numbers together, and all the variables

6x^2-1x-18=0

a = 6; b = -1; c = -18;
Δ = b2-4ac
Δ = -12-4·6·(-18)
Δ = 433
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{433}}{2*6}=\frac{1-\sqrt{433}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{433}}{2*6}=\frac{1+\sqrt{433}}{12}
$