7n^2-7=-12n

Solution for 7n^2-7=-12n equation:

7n^2-7=-12n

We move all terms to the left:

7n^2-7-(-12n)=0

We get rid of parentheses

7n^2+12n-7=0

a = 7; b = 12; c = -7;
Δ = b2-4ac
Δ = 122-4·7·(-7)
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{85}}{2*7}=\frac{-12-2\sqrt{85}}{14}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{85}}{2*7}=\frac{-12+2\sqrt{85}}{14}
$