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X^2-21X-342=0
a = 1; b = -21; c = -342;
Δ = b2-4ac
Δ = -212-4·1·(-342)
Δ = 1809
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1809}=\sqrt{9*201}=\sqrt{9}*\sqrt{201}=3\sqrt{201}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{201}}{2*1}=\frac{21-3\sqrt{201}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{201}}{2*1}=\frac{21+3\sqrt{201}}{2} $
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