5n^2+7=-12n

Solution for 5n^2+7=-12n equation:

5n^2+7=-12n

We move all terms to the left:

5n^2+7-(-12n)=0

We get rid of parentheses

5n^2+12n+7=0

a = 5; b = 12; c = +7;
Δ = b2-4ac
Δ = 122-4·5·7
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2}{2*5}=\frac{-14}{10}
=-1+2/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2}{2*5}=\frac{-10}{10}
=-1
$