2x(x-1)+5=-2x+23

Solution for 2x(x-1)+5=-2x+23 equation:

2x(x-1)+5=-2x+23

We move all terms to the left:

2x(x-1)+5-(-2x+23)=0

We multiply parentheses

2x^2-2x-(-2x+23)+5=0

We get rid of parentheses

2x^2-2x+2x-23+5=0

We add all the numbers together, and all the variables

2x^2-18=0

a = 2; b = 0; c = -18;
Δ = b2-4ac
Δ = 02-4·2·(-18)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12}{2*2}=\frac{-12}{4}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12}{2*2}=\frac{12}{4}
=3
$