n^2+29n/7-30/7=0

Solution for n^2+29n/7-30/7=0 equation:

n^2+29n/7-30/7=0

We multiply all the terms by the denominator


n^2*7+29n-30=0

Wy multiply elements

7n^2+29n-30=0

a = 7; b = 29; c = -30;
Δ = b2-4ac
Δ = 292-4·7·(-30)
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*7}=\frac{-70}{14}
=-5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+41}{2*7}=\frac{12}{14}
=6/7
$