4/3x-7/2x=91/12

Solution for 4/3x-7/2x=91/12 equation:

4/3x-7/2x=91/12

We move all terms to the left:

4/3x-7/2x-(91/12)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

4/3x-7/2x-(+91/12)=0

We get rid of parentheses

4/3x-7/2x-91/12=0

We calculate fractions


(-1092x^2)/72x^2+96x/72x^2+(-252x)/72x^2=0

We multiply all the terms by the denominator


(-1092x^2)+96x+(-252x)=0

We get rid of parentheses

-1092x^2+96x-252x=0

We add all the numbers together, and all the variables

-1092x^2-156x=0

a = -1092; b = -156; c = 0;
Δ = b2-4ac
Δ = -1562-4·(-1092)·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*-1092}=\frac{0}{-2184}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-156)+156}{2*-1092}=\frac{312}{-2184}
=-1/7
$