6n^2-2n-3=5n^2-9n-6

Solution for 6n^2-2n-3=5n^2-9n-6 equation:

6n^2-2n-3=5n^2-9n-6

We move all terms to the left:

6n^2-2n-3-(5n^2-9n-6)=0

We get rid of parentheses

6n^2-5n^2-2n+9n+6-3=0

We add all the numbers together, and all the variables

n^2+7n+3=0

a = 1; b = 7; c = +3;
Δ = b2-4ac
Δ = 72-4·1·3
Δ = 37
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{37}}{2*1}=\frac{-7-\sqrt{37}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{37}}{2*1}=\frac{-7+\sqrt{37}}{2}
$