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-13a^2+18a+412=0
a = -13; b = 18; c = +412;
Δ = b2-4ac
Δ = 182-4·(-13)·412
Δ = 21748
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{21748}=\sqrt{4*5437}=\sqrt{4}*\sqrt{5437}=2\sqrt{5437}$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{5437}}{2*-13}=\frac{-18-2\sqrt{5437}}{-26} $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{5437}}{2*-13}=\frac{-18+2\sqrt{5437}}{-26} $
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