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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x-3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


6x/2x^2+(-8x)/2x^2+3+4=0

We add all the numbers together, and all the variables

6x/2x^2+(-8x)/2x^2+7=0

We multiply all the terms by the denominator


6x+(-8x)+7*2x^2=0

Wy multiply elements

14x^2+6x+(-8x)=0

We get rid of parentheses

14x^2+6x-8x=0

We add all the numbers together, and all the variables

14x^2-2x=0

a = 14; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·14·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*14}=\frac{0}{28}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*14}=\frac{4}{28}
=1/7
$