n^2+11n-43=-2n^2-1

Solution for n^2+11n-43=-2n^2-1 equation:

n^2+11n-43=-2n^2-1

We move all terms to the left:

n^2+11n-43-(-2n^2-1)=0

We get rid of parentheses

n^2+2n^2+11n+1-43=0

We add all the numbers together, and all the variables

3n^2+11n-42=0

a = 3; b = 11; c = -42;
Δ = b2-4ac
Δ = 112-4·3·(-42)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-25}{2*3}=\frac{-36}{6}
=-6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+25}{2*3}=\frac{14}{6}
=2+1/3
$