12n^2-14n=66-7n+7n^2

Solution for 12n^2-14n=66-7n+7n^2 equation:

12n^2-14n=66-7n+7n^2

We move all terms to the left:

12n^2-14n-(66-7n+7n^2)=0

We get rid of parentheses

12n^2-7n^2+7n-14n-66=0

We add all the numbers together, and all the variables

5n^2-7n-66=0

a = 5; b = -7; c = -66;
Δ = b2-4ac
Δ = -72-4·5·(-66)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-37}{2*5}=\frac{-30}{10}
=-3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+37}{2*5}=\frac{44}{10}
=4+2/5
$