-9n^2=-4n-19

Solution for -9n^2=-4n-19 equation:

-9n^2=-4n-19

We move all terms to the left:

-9n^2-(-4n-19)=0

We get rid of parentheses

-9n^2+4n+19=0

a = -9; b = 4; c = +19;
Δ = b2-4ac
Δ = 42-4·(-9)·19
Δ = 700
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:

$\sqrt{\Delta}=\sqrt{700}=\sqrt{100*7}=\sqrt{100}*\sqrt{7}=10\sqrt{7}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-10\sqrt{7}}{2*-9}=\frac{-4-10\sqrt{7}}{-18}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+10\sqrt{7}}{2*-9}=\frac{-4+10\sqrt{7}}{-18}
$