5n^2-3n=-8n

Solution for 5n^2-3n=-8n equation:

5n^2-3n=-8n

We move all terms to the left:

5n^2-3n-(-8n)=0

We get rid of parentheses

5n^2-3n+8n=0

We add all the numbers together, and all the variables

5n^2+5n=0

a = 5; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·5·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*5}=\frac{-10}{10}
=-1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*5}=\frac{0}{10}
=0
$