5n^2+19n=12

Solution for 5n^2+19n=12 equation:

5n^2+19n=12

We move all terms to the left:

5n^2+19n-(12)=0

a = 5; b = 19; c = -12;
Δ = b2-4ac
Δ = 192-4·5·(-12)
Δ = 601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-\sqrt{601}}{2*5}=\frac{-19-\sqrt{601}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{601}}{2*5}=\frac{-19+\sqrt{601}}{10}
$