-3(n2)-9=n-22

Solution for -3(n2)-9=n-22 equation:

-3(n2)-9=n-22

We move all terms to the left:

-3(n2)-9-(n-22)=0

We add all the numbers together, and all the variables

-3n^2-(n-22)-9=0

We get rid of parentheses

-3n^2-n+22-9=0

We add all the numbers together, and all the variables

-3n^2-1n+13=0

a = -3; b = -1; c = +13;
Δ = b2-4ac
Δ = -12-4·(-3)·13
Δ = 157
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{-(-1)-\sqrt{157}}{2*-3}=\frac{1-\sqrt{157}}{-6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{157}}{2*-3}=\frac{1+\sqrt{157}}{-6}
$