10n^2+78n-108=0

Solution for 10n^2+78n-108=0 equation:

10n^2+78n-108=0

a = 10; b = 78; c = -108;
Δ = b2-4ac
Δ = 782-4·10·(-108)
Δ = 10404
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10404}=102$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-102}{2*10}=\frac{-180}{20}
=-9
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+102}{2*10}=\frac{24}{20}
=1+1/5
$