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18x^2+21x-221=0
a = 18; b = 21; c = -221;
Δ = b2-4ac
Δ = 212-4·18·(-221)
Δ = 16353
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{16353}=\sqrt{9*1817}=\sqrt{9}*\sqrt{1817}=3\sqrt{1817}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{1817}}{2*18}=\frac{-21-3\sqrt{1817}}{36} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{1817}}{2*18}=\frac{-21+3\sqrt{1817}}{36} $
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