3n^2=-29n-56

Solution for 3n^2=-29n-56 equation:

3n^2=-29n-56

We move all terms to the left:

3n^2-(-29n-56)=0

We get rid of parentheses

3n^2+29n+56=0

a = 3; b = 29; c = +56;
Δ = b2-4ac
Δ = 292-4·3·56
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-13}{2*3}=\frac{-42}{6}
=-7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+13}{2*3}=\frac{-16}{6}
=-2+2/3
$