-3n^2+13n-3=8n-5n^2

Solution for -3n^2+13n-3=8n-5n^2 equation:

-3n^2+13n-3=8n-5n^2

We move all terms to the left:

-3n^2+13n-3-(8n-5n^2)=0

We get rid of parentheses

-3n^2+5n^2-8n+13n-3=0

We add all the numbers together, and all the variables

2n^2+5n-3=0

a = 2; b = 5; c = -3;
Δ = b2-4ac
Δ = 52-4·2·(-3)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-7}{2*2}=\frac{-12}{4}
=-3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+7}{2*2}=\frac{2}{4}
=1/2
$