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

We add all the numbers together, and all the variables

5n^2-19n+12=0

a = 5; b = -19; c = +12;
Δ = b2-4ac
Δ = -192-4·5·12
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-11}{2*5}=\frac{8}{10}
=4/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+11}{2*5}=\frac{30}{10}
=3
$