0=5n^2-n-238

Solution for 0=5n^2-n-238 equation:

0=5n^2-n-238

We move all terms to the left:

0-(5n^2-n-238)=0

We add all the numbers together, and all the variables

-(5n^2-n-238)=0

We get rid of parentheses

-5n^2+n+238=0

a = -5; b = 1; c = +238;
Δ = b2-4ac
Δ = 12-4·(-5)·238
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-69}{2*-5}=\frac{-70}{-10}
=+7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+69}{2*-5}=\frac{68}{-10}
=-6+4/5
$