5n^2=-32n-35

Solution for 5n^2=-32n-35 equation:

5n^2=-32n-35

We move all terms to the left:

5n^2-(-32n-35)=0

We get rid of parentheses

5n^2+32n+35=0

a = 5; b = 32; c = +35;
Δ = b2-4ac
Δ = 322-4·5·35
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-18}{2*5}=\frac{-50}{10}
=-5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+18}{2*5}=\frac{-14}{10}
=-1+2/5
$