4x(23-x)=4

Solution for 4x(23-x)=4 equation:

4x(23-x)=4

We move all terms to the left:

4x(23-x)-(4)=0

We add all the numbers together, and all the variables

4x(-1x+23)-4=0

We multiply parentheses

-4x^2+92x-4=0

a = -4; b = 92; c = -4;
Δ = b2-4ac
Δ = 922-4·(-4)·(-4)
Δ = 8400
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:

$\sqrt{\Delta}=\sqrt{8400}=\sqrt{400*21}=\sqrt{400}*\sqrt{21}=20\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(92)-20\sqrt{21}}{2*-4}=\frac{-92-20\sqrt{21}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(92)+20\sqrt{21}}{2*-4}=\frac{-92+20\sqrt{21}}{-8}
$