4/x+3=2/8x-1

Solution for 4/x+3=2/8x-1 equation:

4/x+3=2/8x-1

We move all terms to the left:

4/x+3-(2/8x-1)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 8x-1)!=0

x∈R


We get rid of parentheses

4/x-2/8x+1+3=0

We calculate fractions


32x/8x^2+(-2x)/8x^2+1+3=0

We add all the numbers together, and all the variables

32x/8x^2+(-2x)/8x^2+4=0

We multiply all the terms by the denominator


32x+(-2x)+4*8x^2=0

Wy multiply elements

32x^2+32x+(-2x)=0

We get rid of parentheses

32x^2+32x-2x=0

We add all the numbers together, and all the variables

32x^2+30x=0

a = 32; b = 30; c = 0;
Δ = b2-4ac
Δ = 302-4·32·0
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*32}=\frac{-60}{64}
=-15/16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30}{2*32}=\frac{0}{64}
=0
$