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X^2+24X-420=0
a = 1; b = 24; c = -420;
Δ = b2-4ac
Δ = 242-4·1·(-420)
Δ = 2256
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2256}=\sqrt{16*141}=\sqrt{16}*\sqrt{141}=4\sqrt{141}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{141}}{2*1}=\frac{-24-4\sqrt{141}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{141}}{2*1}=\frac{-24+4\sqrt{141}}{2} $
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