18x=6/12x+18

Solution for 18x=6/12x+18 equation:

18x=6/12x+18

We move all terms to the left:

18x-(6/12x+18)=0


Domain of the equation: 12x+18)!=0

x∈R


We get rid of parentheses

18x-6/12x-18=0

We multiply all the terms by the denominator


18x*12x-18*12x-6=0

Wy multiply elements

216x^2-216x-6=0

a = 216; b = -216; c = -6;
Δ = b2-4ac
Δ = -2162-4·216·(-6)
Δ = 51840
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:

$\sqrt{\Delta}=\sqrt{51840}=\sqrt{5184*10}=\sqrt{5184}*\sqrt{10}=72\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-216)-72\sqrt{10}}{2*216}=\frac{216-72\sqrt{10}}{432}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-216)+72\sqrt{10}}{2*216}=\frac{216+72\sqrt{10}}{432}
$