2/8x=5/5x+4

Solution for 2/8x=5/5x+4 equation:

2/8x=5/5x+4

We move all terms to the left:

2/8x-(5/5x+4)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



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

x∈R


We get rid of parentheses

2/8x-5/5x-4=0

We calculate fractions


10x/40x^2+(-40x)/40x^2-4=0

We multiply all the terms by the denominator


10x+(-40x)-4*40x^2=0

Wy multiply elements

-160x^2+10x+(-40x)=0

We get rid of parentheses

-160x^2+10x-40x=0

We add all the numbers together, and all the variables

-160x^2-30x=0

a = -160; b = -30; c = 0;
Δ = b2-4ac
Δ = -302-4·(-160)·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-30}{2*-160}=\frac{0}{-320}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+30}{2*-160}=\frac{60}{-320}
=-3/16
$