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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 6x+3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


18x/24x^2+(-8x)/24x^2-3-6=0

We add all the numbers together, and all the variables

18x/24x^2+(-8x)/24x^2-9=0

We multiply all the terms by the denominator


18x+(-8x)-9*24x^2=0

Wy multiply elements

-216x^2+18x+(-8x)=0

We get rid of parentheses

-216x^2+18x-8x=0

We add all the numbers together, and all the variables

-216x^2+10x=0

a = -216; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-216)·0
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{-(10)-10}{2*-216}=\frac{-20}{-432}
=5/108
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-216}=\frac{0}{-432}
=0
$