3x+5/2x=1/2x-8

Solution for 3x+5/2x=1/2x-8 equation:

3x+5/2x=1/2x-8

We move all terms to the left:

3x+5/2x-(1/2x-8)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 2x-8)!=0

x∈R


We get rid of parentheses

3x+5/2x-1/2x+8=0

We multiply all the terms by the denominator


3x*2x+8*2x+5-1=0

We add all the numbers together, and all the variables

3x*2x+8*2x+4=0

Wy multiply elements

6x^2+16x+4=0

a = 6; b = 16; c = +4;
Δ = b2-4ac
Δ = 162-4·6·4
Δ = 160
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{10}}{2*6}=\frac{-16-4\sqrt{10}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{10}}{2*6}=\frac{-16+4\sqrt{10}}{12}
$