5n2+3n-1=1

Solution for 5n2+3n-1=1 equation:

5n^2+3n-1=1

We move all terms to the left:

5n^2+3n-1-(1)=0

We add all the numbers together, and all the variables

5n^2+3n-2=0

a = 5; b = 3; c = -2;
Δ = b2-4ac
Δ = 32-4·5·(-2)
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{-(3)-7}{2*5}=\frac{-10}{10}
=-1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+7}{2*5}=\frac{4}{10}
=2/5
$