8x(4-x)=23

Solution for 8x(4-x)=23 equation:

8x(4-x)=23

We move all terms to the left:

8x(4-x)-(23)=0

We add all the numbers together, and all the variables

8x(-1x+4)-23=0

We multiply parentheses

-8x^2+32x-23=0

a = -8; b = 32; c = -23;
Δ = b2-4ac
Δ = 322-4·(-8)·(-23)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-12\sqrt{2}}{2*-8}=\frac{-32-12\sqrt{2}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+12\sqrt{2}}{2*-8}=\frac{-32+12\sqrt{2}}{-16}
$