4x(8-x)=x+4

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

4x(8-x)=x+4

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-4x^2+32x-(x+4)=0

We get rid of parentheses

-4x^2+32x-x-4=0

We add all the numbers together, and all the variables

-4x^2+31x-4=0

a = -4; b = 31; c = -4;
Δ = b2-4ac
Δ = 312-4·(-4)·(-4)
Δ = 897
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{-(31)-\sqrt{897}}{2*-4}=\frac{-31-\sqrt{897}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+\sqrt{897}}{2*-4}=\frac{-31+\sqrt{897}}{-8}
$