4x(-4-x)=5x

Solution for 4x(-4-x)=5x equation:

4x(-4-x)=5x

We move all terms to the left:

4x(-4-x)-(5x)=0

We add all the numbers together, and all the variables

4x(-1x-4)-5x=0

We add all the numbers together, and all the variables

-5x+4x(-1x-4)=0

We multiply parentheses

-4x^2-5x-16x=0

We add all the numbers together, and all the variables

-4x^2-21x=0

a = -4; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·(-4)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21}{2*-4}=\frac{0}{-8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*-4}=\frac{42}{-8}
=-5+1/4
$