2x^2-15x-23=2x

Solution for 2x^2-15x-23=2x equation:

2x^2-15x-23=2x

We move all terms to the left:

2x^2-15x-23-(2x)=0

We add all the numbers together, and all the variables

2x^2-17x-23=0

a = 2; b = -17; c = -23;
Δ = b2-4ac
Δ = -172-4·2·(-23)
Δ = 473
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{-(-17)-\sqrt{473}}{2*2}=\frac{17-\sqrt{473}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{473}}{2*2}=\frac{17+\sqrt{473}}{4}
$