10/5x=8x*4

Solution for 10/5x=8x*4 equation:

10/5x=8x*4

We move all terms to the left:

10/5x-(8x*4)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

10/5x-(+8x*4)=0

We get rid of parentheses

10/5x-8x*4=0

We multiply all the terms by the denominator


-(8x*4)*5x+10=0

We add all the numbers together, and all the variables

-(+8x*4)*5x+10=0

We multiply parentheses

-160x^2+10=0

a = -160; b = 0; c = +10;
Δ = b2-4ac
Δ = 02-4·(-160)·10
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80}{2*-160}=\frac{-80}{-320}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80}{2*-160}=\frac{80}{-320}
=-1/4
$