4x-9)/12=3x+7)/12

Solution for 4x-9)/12=3x+7)/12 equation:

4x-9)/12=3x+7)/12

We move all terms to the left:

4x-9)/12-(3x+7)/12)=0


Domain of the equation: 12-(3x!=0

We move all terms containing x to the left, all other terms to the right

-(3x!=-12

x∈R


We calculate fractions


4x+()/(-36x+12)-3x/(-36x+12)+7*12=0

We add all the numbers together, and all the variables

4x+()/(-36x+12)-3x/(-36x+12)+84=0

We multiply all the terms by the denominator


4x*(-36x+12)-3x+84*(-36x+12)+()=0

We add all the numbers together, and all the variables

-3x+4x*(-36x+12)+84*(-36x+12)=0

We multiply parentheses

-144x^2-3x+48x-3024x+1008=0

We add all the numbers together, and all the variables

-144x^2-2979x+1008=0

a = -144; b = -2979; c = +1008;
Δ = b2-4ac
Δ = -29792-4·(-144)·1008
Δ = 9455049
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{9455049}=\sqrt{81*116729}=\sqrt{81}*\sqrt{116729}=9\sqrt{116729}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2979)-9\sqrt{116729}}{2*-144}=\frac{2979-9\sqrt{116729}}{-288}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2979)+9\sqrt{116729}}{2*-144}=\frac{2979+9\sqrt{116729}}{-288}
$