-3n^2=-12n-7

Solution for -3n^2=-12n-7 equation:

-3n^2=-12n-7

We move all terms to the left:

-3n^2-(-12n-7)=0

We get rid of parentheses

-3n^2+12n+7=0

a = -3; b = 12; c = +7;
Δ = b2-4ac
Δ = 122-4·(-3)·7
Δ = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{57}}{2*-3}=\frac{-12-2\sqrt{57}}{-6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{57}}{2*-3}=\frac{-12+2\sqrt{57}}{-6}
$