X/3x-12=24-9x

Solution for X/3x-12=24-9x equation:

X/3X-12=24-9X

We move all terms to the left:

X/3X-12-(24-9X)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We add all the numbers together, and all the variables

X/3X-(-9X+24)-12=0

We get rid of parentheses

X/3X+9X-24-12=0

We multiply all the terms by the denominator


X+9X*3X-24*3X-12*3X=0

Wy multiply elements

27X^2+X-72X-36X=0

We add all the numbers together, and all the variables

27X^2-107X=0

a = 27; b = -107; c = 0;
Δ = b2-4ac
Δ = -1072-4·27·0
Δ = 11449
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11449}=107$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-107)-107}{2*27}=\frac{0}{54}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-107)+107}{2*27}=\frac{214}{54}
=3+26/27
$