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18x^2-24x+32-162=0
We add all the numbers together, and all the variables
18x^2-24x-130=0
a = 18; b = -24; c = -130;
Δ = b2-4ac
Δ = -242-4·18·(-130)
Δ = 9936
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{9936}=\sqrt{144*69}=\sqrt{144}*\sqrt{69}=12\sqrt{69}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12\sqrt{69}}{2*18}=\frac{24-12\sqrt{69}}{36} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12\sqrt{69}}{2*18}=\frac{24+12\sqrt{69}}{36} $
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