3n+4=n+5X2

Solution for 3n+4=n+5X2 equation:

3n+4=n+5n^2

We move all terms to the left:

3n+4-(n+5n^2)=0

We get rid of parentheses

-5n^2-n+3n+4=0

We add all the numbers together, and all the variables

-5n^2+2n+4=0

a = -5; b = 2; c = +4;
Δ = b2-4ac
Δ = 22-4·(-5)·4
Δ = 84
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{21}}{2*-5}=\frac{-2-2\sqrt{21}}{-10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{21}}{2*-5}=\frac{-2+2\sqrt{21}}{-10}
$