(2n)(2)=3n-1/5

Solution for (2n)(2)=3n-1/5 equation:

(2n)(2)=3n-1/5

We move all terms to the left:

(2n)(2)-(3n-1/5)=0

We add all the numbers together, and all the variables

2n2-(+3n-1/5)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

2n^2-3n+1/5=0

We multiply all the terms by the denominator


2n^2*5-3n*5+1=0

Wy multiply elements

10n^2-15n+1=0

a = 10; b = -15; c = +1;
Δ = b2-4ac
Δ = -152-4·10·1
Δ = 185
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{185}}{2*10}=\frac{15-\sqrt{185}}{20}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{185}}{2*10}=\frac{15+\sqrt{185}}{20}
$