13n^2=-12n+180

Solution for 13n^2=-12n+180 equation:

13n^2=-12n+180

We move all terms to the left:

13n^2-(-12n+180)=0

We get rid of parentheses

13n^2+12n-180=0

a = 13; b = 12; c = -180;
Δ = b2-4ac
Δ = 122-4·13·(-180)
Δ = 9504
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:

$\sqrt{\Delta}=\sqrt{9504}=\sqrt{144*66}=\sqrt{144}*\sqrt{66}=12\sqrt{66}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{66}}{2*13}=\frac{-12-12\sqrt{66}}{26}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{66}}{2*13}=\frac{-12+12\sqrt{66}}{26}
$