10n^2+9n-6=6+7n^2

Solution for 10n^2+9n-6=6+7n^2 equation:

10n^2+9n-6=6+7n^2

We move all terms to the left:

10n^2+9n-6-(6+7n^2)=0

We get rid of parentheses

10n^2-7n^2+9n-6-6=0

We add all the numbers together, and all the variables

3n^2+9n-12=0

a = 3; b = 9; c = -12;
Δ = b2-4ac
Δ = 92-4·3·(-12)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-15}{2*3}=\frac{-24}{6}
=-4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+15}{2*3}=\frac{6}{6}
=1
$