6n^2-37n-42=-8n^2

Solution for 6n^2-37n-42=-8n^2 equation:

6n^2-37n-42=-8n^2

We move all terms to the left:

6n^2-37n-42-(-8n^2)=0

We get rid of parentheses

6n^2+8n^2-37n-42=0

We add all the numbers together, and all the variables

14n^2-37n-42=0

a = 14; b = -37; c = -42;
Δ = b2-4ac
Δ = -372-4·14·(-42)
Δ = 3721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3721}=61$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-61}{2*14}=\frac{-24}{28}
=-6/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+61}{2*14}=\frac{98}{28}
=3+1/2
$