5n^2=42+29n

Solution for 5n^2=42+29n equation:

5n^2=42+29n

We move all terms to the left:

5n^2-(42+29n)=0

We add all the numbers together, and all the variables

5n^2-(29n+42)=0

We get rid of parentheses

5n^2-29n-42=0

a = 5; b = -29; c = -42;
Δ = b2-4ac
Δ = -292-4·5·(-42)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-41}{2*5}=\frac{-12}{10}
=-1+1/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+41}{2*5}=\frac{70}{10}
=7
$