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x^2+74x+420=0
a = 1; b = 74; c = +420;
Δ = b2-4ac
Δ = 742-4·1·420
Δ = 3796
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3796}=\sqrt{4*949}=\sqrt{4}*\sqrt{949}=2\sqrt{949}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(74)-2\sqrt{949}}{2*1}=\frac{-74-2\sqrt{949}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(74)+2\sqrt{949}}{2*1}=\frac{-74+2\sqrt{949}}{2} $
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