10n^2+10n-15=0

Solution for 10n^2+10n-15=0 equation:

10n^2+10n-15=0

a = 10; b = 10; c = -15;
Δ = b2-4ac
Δ = 102-4·10·(-15)
Δ = 700
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:

$\sqrt{\Delta}=\sqrt{700}=\sqrt{100*7}=\sqrt{100}*\sqrt{7}=10\sqrt{7}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{7}}{2*10}=\frac{-10-10\sqrt{7}}{20}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{7}}{2*10}=\frac{-10+10\sqrt{7}}{20}
$