0=8x-5/5x+4

Solution for 0=8x-5/5x+4 equation:

0=8x-5/5x+4

We move all terms to the left:

0-(8x-5/5x+4)=0


Domain of the equation: 5x+4)!=0

x∈R


We add all the numbers together, and all the variables

-(8x-5/5x+4)=0

We get rid of parentheses

-8x+5/5x-4=0

We multiply all the terms by the denominator


-8x*5x-4*5x+5=0

Wy multiply elements

-40x^2-20x+5=0

a = -40; b = -20; c = +5;
Δ = b2-4ac
Δ = -202-4·(-40)·5
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20\sqrt{3}}{2*-40}=\frac{20-20\sqrt{3}}{-80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20\sqrt{3}}{2*-40}=\frac{20+20\sqrt{3}}{-80}
$