3/2x-8=4/8x-6

Solution for 3/2x-8=4/8x-6 equation:

3/2x-8=4/8x-6

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 8x-6)!=0

x∈R


We get rid of parentheses

3/2x-4/8x+6-8=0

We calculate fractions


24x/16x^2+(-8x)/16x^2+6-8=0

We add all the numbers together, and all the variables

24x/16x^2+(-8x)/16x^2-2=0

We multiply all the terms by the denominator


24x+(-8x)-2*16x^2=0

Wy multiply elements

-32x^2+24x+(-8x)=0

We get rid of parentheses

-32x^2+24x-8x=0

We add all the numbers together, and all the variables

-32x^2+16x=0

a = -32; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-32)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-32}=\frac{-32}{-64}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-32}=\frac{0}{-64}
=0
$