3/2x-5=4/6x+7

Solution for 3/2x-5=4/6x+7 equation:

3/2x-5=4/6x+7

We move all terms to the left:

3/2x-5-(4/6x+7)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 6x+7)!=0

x∈R


We get rid of parentheses

3/2x-4/6x-7-5=0

We calculate fractions


18x/12x^2+(-8x)/12x^2-7-5=0

We add all the numbers together, and all the variables

18x/12x^2+(-8x)/12x^2-12=0

We multiply all the terms by the denominator


18x+(-8x)-12*12x^2=0

Wy multiply elements

-144x^2+18x+(-8x)=0

We get rid of parentheses

-144x^2+18x-8x=0

We add all the numbers together, and all the variables

-144x^2+10x=0

a = -144; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-144)·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*-144}=\frac{-20}{-288}
=5/72
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-144}=\frac{0}{-288}
=0
$