5x=8/x-20=2

Solution for 5x=8/x-20=2 equation:

5x=8/x-20=2

We move all terms to the left:

5x-(8/x-20)=0


Domain of the equation: x-20)!=0

x∈R


We get rid of parentheses

5x-8/x+20=0

We multiply all the terms by the denominator


5x*x+20*x-8=0

We add all the numbers together, and all the variables

20x+5x*x-8=0

Wy multiply elements

5x^2+20x-8=0

a = 5; b = 20; c = -8;
Δ = b2-4ac
Δ = 202-4·5·(-8)
Δ = 560
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:

$\sqrt{\Delta}=\sqrt{560}=\sqrt{16*35}=\sqrt{16}*\sqrt{35}=4\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{35}}{2*5}=\frac{-20-4\sqrt{35}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{35}}{2*5}=\frac{-20+4\sqrt{35}}{10}
$