45-(9n+7)n=2

Solution for 45-(9n+7)n=2 equation:

45-(9n+7)n=2

We move all terms to the left:

45-(9n+7)n-(2)=0

We add all the numbers together, and all the variables

-(9n+7)n+43=0

We multiply parentheses

-9n^2-7n+43=0

a = -9; b = -7; c = +43;
Δ = b2-4ac
Δ = -72-4·(-9)·43
Δ = 1597
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{-(-7)-\sqrt{1597}}{2*-9}=\frac{7-\sqrt{1597}}{-18}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{1597}}{2*-9}=\frac{7+\sqrt{1597}}{-18}
$