X(80-0.75x)=4x

Solution for X(80-0.75x)=4x equation:

X(80-0.75X)=4X

We move all terms to the left:

X(80-0.75X)-(4X)=0

We add all the numbers together, and all the variables

X(-0.75X+80)-4X=0

We add all the numbers together, and all the variables

-4X+X(-0.75X+80)=0

We multiply parentheses

0X^2-4X+80X=0

We add all the numbers together, and all the variables

X^2+76X=0

a = 1; b = 76; c = 0;
Δ = b2-4ac
Δ = 762-4·1·0
Δ = 5776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5776}=76$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(76)-76}{2*1}=\frac{-152}{2}
=-76
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(76)+76}{2*1}=\frac{0}{2}
=0
$