5n^2=48-34n

Solution for 5n^2=48-34n equation:

5n^2=48-34n

We move all terms to the left:

5n^2-(48-34n)=0

We add all the numbers together, and all the variables

5n^2-(-34n+48)=0

We get rid of parentheses

5n^2+34n-48=0

a = 5; b = 34; c = -48;
Δ = b2-4ac
Δ = 342-4·5·(-48)
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-46}{2*5}=\frac{-80}{10}
=-8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+46}{2*5}=\frac{12}{10}
=1+1/5
$