(40x-16x^2)/(x-x^2)=8

Solution for (40x-16x^2)/(x-x^2)=8 equation:

(40x-16x^2)/(x-x^2)=8

We move all terms to the left:

(40x-16x^2)/(x-x^2)-(8)=0


Domain of the equation: (x-x^2)!=0

x∈R


We multiply all the terms by the denominator


(40x-16x^2)-8*(x-x^2)=0

We multiply parentheses

(40x-16x^2)+8x^2-8x=0

We get rid of parentheses

-16x^2+8x^2+40x-8x=0

We add all the numbers together, and all the variables

-8x^2+32x=0

a = -8; b = 32; c = 0;
Δ = b2-4ac
Δ = 322-4·(-8)·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-32}{2*-8}=\frac{-64}{-16}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+32}{2*-8}=\frac{0}{-16}
=0
$