6x^2-x=22

Solution for 6x^2-x=22 equation:

6x^2-x=22

We move all terms to the left:

6x^2-x-(22)=0

We add all the numbers together, and all the variables

6x^2-1x-22=0

a = 6; b = -1; c = -22;
Δ = b2-4ac
Δ = -12-4·6·(-22)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-23}{2*6}=\frac{-22}{12}
=-1+5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+23}{2*6}=\frac{24}{12}
=2
$