x/5x+20=2x+8

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

x/5x+20=2x+8

We move all terms to the left:

x/5x+20-(2x+8)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

x/5x-2x-8+20=0

We multiply all the terms by the denominator


x-2x*5x-8*5x+20*5x=0

Wy multiply elements

-10x^2+x-40x+100x=0

We add all the numbers together, and all the variables

-10x^2+61x=0

a = -10; b = 61; c = 0;
Δ = b2-4ac
Δ = 612-4·(-10)·0
Δ = 3721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3721}=61$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(61)-61}{2*-10}=\frac{-122}{-20}
=6+1/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(61)+61}{2*-10}=\frac{0}{-20}
=0
$