7/2x-4/3x=13/12

Solution for 7/2x-4/3x=13/12 equation:

7/2x-4/3x=13/12

We move all terms to the left:

7/2x-4/3x-(13/12)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

7/2x-4/3x-(+13/12)=0

We get rid of parentheses

7/2x-4/3x-13/12=0

We calculate fractions


(-234x^2)/72x^2+252x/72x^2+(-96x)/72x^2=0

We multiply all the terms by the denominator


(-234x^2)+252x+(-96x)=0

We get rid of parentheses

-234x^2+252x-96x=0

We add all the numbers together, and all the variables

-234x^2+156x=0

a = -234; b = 156; c = 0;
Δ = b2-4ac
Δ = 1562-4·(-234)·0
Δ = 24336
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{24336}=156$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(156)-156}{2*-234}=\frac{-312}{-468}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(156)+156}{2*-234}=\frac{0}{-468}
=0
$