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338x^2-218x-72=0
a = 338; b = -218; c = -72;
Δ = b2-4ac
Δ = -2182-4·338·(-72)
Δ = 144868
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{144868}=\sqrt{4*36217}=\sqrt{4}*\sqrt{36217}=2\sqrt{36217}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-218)-2\sqrt{36217}}{2*338}=\frac{218-2\sqrt{36217}}{676} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-218)+2\sqrt{36217}}{2*338}=\frac{218+2\sqrt{36217}}{676} $
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