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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(-4x^2+46x+2x-23)-23=0

We get rid of parentheses

-4x^2+46x+2x-23-23=0

We add all the numbers together, and all the variables

-4x^2+48x-46=0

a = -4; b = 48; c = -46;
Δ = b2-4ac
Δ = 482-4·(-4)·(-46)
Δ = 1568
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1568}=\sqrt{784*2}=\sqrt{784}*\sqrt{2}=28\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-28\sqrt{2}}{2*-4}=\frac{-48-28\sqrt{2}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+28\sqrt{2}}{2*-4}=\frac{-48+28\sqrt{2}}{-8}
$