6/1+x=8/2x-3

Solution for 6/1+x=8/2x-3 equation:

6/1+x=8/2x-3

We move all terms to the left:

6/1+x-(8/2x-3)=0


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

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

x-8/2x+3=0

We multiply all the terms by the denominator


x*2x+3*2x-8=0

Wy multiply elements

2x^2+6x-8=0

a = 2; b = 6; c = -8;
Δ = b2-4ac
Δ = 62-4·2·(-8)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-10}{2*2}=\frac{-16}{4}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+10}{2*2}=\frac{4}{4}
=1
$