2x^2-x=22.5

Solution for 2x^2-x=22.5 equation:

2x^2-x=22.5

We move all terms to the left:

2x^2-x-(22.5)=0

We add all the numbers together, and all the variables

2x^2-1x-22.5=0

a = 2; b = -1; c = -22.5;
Δ = b2-4ac
Δ = -12-4·2·(-22.5)
Δ = 181
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{181}}{2*2}=\frac{1-\sqrt{181}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{181}}{2*2}=\frac{1+\sqrt{181}}{4}
$