4n^2=-12n-7

Solution for 4n^2=-12n-7 equation:

4n^2=-12n-7

We move all terms to the left:

4n^2-(-12n-7)=0

We get rid of parentheses

4n^2+12n+7=0

a = 4; b = 12; c = +7;
Δ = b2-4ac
Δ = 122-4·4·7
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{2}}{2*4}=\frac{-12-4\sqrt{2}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{2}}{2*4}=\frac{-12+4\sqrt{2}}{8}
$