8n^2-3n-180=0

Solution for 8n^2-3n-180=0 equation:

8n^2-3n-180=0

a = 8; b = -3; c = -180;
Δ = b2-4ac
Δ = -32-4·8·(-180)
Δ = 5769
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:

$\sqrt{\Delta}=\sqrt{5769}=\sqrt{9*641}=\sqrt{9}*\sqrt{641}=3\sqrt{641}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{641}}{2*8}=\frac{3-3\sqrt{641}}{16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{641}}{2*8}=\frac{3+3\sqrt{641}}{16}
$