2x^2-x=23

Solution for 2x^2-x=23 equation:

2x^2-x=23

We move all terms to the left:

2x^2-x-(23)=0

We add all the numbers together, and all the variables

2x^2-1x-23=0

a = 2; b = -1; c = -23;
Δ = b2-4ac
Δ = -12-4·2·(-23)
Δ = 185
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{185}}{2*2}=\frac{1-\sqrt{185}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{185}}{2*2}=\frac{1+\sqrt{185}}{4}
$