9x-3/4x=12-6x

Solution for 9x-3/4x=12-6x equation:

9x-3/4x=12-6x

We move all terms to the left:

9x-3/4x-(12-6x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

9x-3/4x-(-6x+12)=0

We get rid of parentheses

9x-3/4x+6x-12=0

We multiply all the terms by the denominator


9x*4x+6x*4x-12*4x-3=0

Wy multiply elements

36x^2+24x^2-48x-3=0

We add all the numbers together, and all the variables

60x^2-48x-3=0

a = 60; b = -48; c = -3;
Δ = b2-4ac
Δ = -482-4·60·(-3)
Δ = 3024
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:

$\sqrt{\Delta}=\sqrt{3024}=\sqrt{144*21}=\sqrt{144}*\sqrt{21}=12\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-12\sqrt{21}}{2*60}=\frac{48-12\sqrt{21}}{120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+12\sqrt{21}}{2*60}=\frac{48+12\sqrt{21}}{120}
$