4/3x=6x+12

Solution for 4/3x=6x+12 equation:

4/3x=6x+12

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

4/3x-6x-12=0

We multiply all the terms by the denominator


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

Wy multiply elements

-18x^2-36x+4=0

a = -18; b = -36; c = +4;
Δ = b2-4ac
Δ = -362-4·(-18)·4
Δ = 1584
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:

$\sqrt{\Delta}=\sqrt{1584}=\sqrt{144*11}=\sqrt{144}*\sqrt{11}=12\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-12\sqrt{11}}{2*-18}=\frac{36-12\sqrt{11}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+12\sqrt{11}}{2*-18}=\frac{36+12\sqrt{11}}{-36}
$