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18x=6/12x+18
We move all terms to the left:
18x-(6/12x+18)=0
Domain of the equation: 12x+18)!=0We get rid of parentheses
x∈R
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} $
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