5n^2+15n-290=0

Solution for 5n^2+15n-290=0 equation:

5n^2+15n-290=0

a = 5; b = 15; c = -290;
Δ = b2-4ac
Δ = 152-4·5·(-290)
Δ = 6025
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:

$\sqrt{\Delta}=\sqrt{6025}=\sqrt{25*241}=\sqrt{25}*\sqrt{241}=5\sqrt{241}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-5\sqrt{241}}{2*5}=\frac{-15-5\sqrt{241}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+5\sqrt{241}}{2*5}=\frac{-15+5\sqrt{241}}{10}
$