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18(x-1)12x=-8
We move all terms to the left:
18(x-1)12x-(-8)=0
We add all the numbers together, and all the variables
18(x-1)12x+8=0
We multiply parentheses
216x^2-216x+8=0
a = 216; b = -216; c = +8;
Δ = b2-4ac
Δ = -2162-4·216·8
Δ = 39744
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{39744}=\sqrt{576*69}=\sqrt{576}*\sqrt{69}=24\sqrt{69}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-216)-24\sqrt{69}}{2*216}=\frac{216-24\sqrt{69}}{432} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-216)+24\sqrt{69}}{2*216}=\frac{216+24\sqrt{69}}{432} $
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