6x^2-18x-18=24

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Solution for 6x^2-18x-18=24 equation:



6x^2-18x-18=24
We move all terms to the left:
6x^2-18x-18-(24)=0
We add all the numbers together, and all the variables
6x^2-18x-42=0
a = 6; b = -18; c = -42;
Δ = b2-4ac
Δ = -182-4·6·(-42)
Δ = 1332
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:
$\sqrt{\Delta}=\sqrt{1332}=\sqrt{36*37}=\sqrt{36}*\sqrt{37}=6\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{37}}{2*6}=\frac{18-6\sqrt{37}}{12} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{37}}{2*6}=\frac{18+6\sqrt{37}}{12} $

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