4/9x+12x-8=18

Solution for 4/9x+12x-8=18 equation:

4/9x+12x-8=18

We move all terms to the left:

4/9x+12x-8-(18)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

12x+4/9x-26=0

We multiply all the terms by the denominator


12x*9x-26*9x+4=0

Wy multiply elements

108x^2-234x+4=0

a = 108; b = -234; c = +4;
Δ = b2-4ac
Δ = -2342-4·108·4
Δ = 53028
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:

$\sqrt{\Delta}=\sqrt{53028}=\sqrt{36*1473}=\sqrt{36}*\sqrt{1473}=6\sqrt{1473}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-234)-6\sqrt{1473}}{2*108}=\frac{234-6\sqrt{1473}}{216}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-234)+6\sqrt{1473}}{2*108}=\frac{234+6\sqrt{1473}}{216}
$