2n^2-18n=4-7n^2

Solution for 2n^2-18n=4-7n^2 equation:

2n^2-18n=4-7n^2

We move all terms to the left:

2n^2-18n-(4-7n^2)=0

We get rid of parentheses

2n^2+7n^2-18n-4=0

We add all the numbers together, and all the variables

9n^2-18n-4=0

a = 9; b = -18; c = -4;
Δ = b2-4ac
Δ = -182-4·9·(-4)
Δ = 468
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{13}}{2*9}=\frac{18-6\sqrt{13}}{18}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{13}}{2*9}=\frac{18+6\sqrt{13}}{18}
$