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-10n^2-14n+224=0
a = -10; b = -14; c = +224;
Δ = b2-4ac
Δ = -142-4·(-10)·224
Δ = 9156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{9156}=\sqrt{4*2289}=\sqrt{4}*\sqrt{2289}=2\sqrt{2289}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{2289}}{2*-10}=\frac{14-2\sqrt{2289}}{-20} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{2289}}{2*-10}=\frac{14+2\sqrt{2289}}{-20} $
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