x/5x+4=3x+8

Solution for x/5x+4=3x+8 equation:

x/5x+4=3x+8

We move all terms to the left:

x/5x+4-(3x+8)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

x/5x-3x-8+4=0

We multiply all the terms by the denominator


x-3x*5x-8*5x+4*5x=0

Wy multiply elements

-15x^2+x-40x+20x=0

We add all the numbers together, and all the variables

-15x^2-19x=0

a = -15; b = -19; c = 0;
Δ = b2-4ac
Δ = -192-4·(-15)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-19}{2*-15}=\frac{0}{-30}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+19}{2*-15}=\frac{38}{-30}
=-1+4/15
$