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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


3x-8x*2x-3*2x-6*2x=0

Wy multiply elements

-16x^2+3x-6x-12x=0

We add all the numbers together, and all the variables

-16x^2-15x=0

a = -16; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·(-16)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*-16}=\frac{0}{-32}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*-16}=\frac{30}{-32}
=-15/16
$