5n+0.56234=4/n+0.412357

Solution for 5n+0.56234=4/n+0.412357 equation:

5n+0.56234=4/n+0.412357

We move all terms to the left:

5n+0.56234-(4/n+0.412357)=0


Domain of the equation: n+0.412357)!=0

n∈R


We get rid of parentheses

5n-4/n-0.412357+0.56234=0

We multiply all the terms by the denominator


5n*n-(0.412357)*n+(0.56234)*n-4=0

We multiply parentheses

5n*n-0.412357n+0.56234n-4=0

Wy multiply elements

5n^2-0.412357n+0.56234n-4=0

We add all the numbers together, and all the variables

5n^2+0.149983n-4=0

a = 5; b = 0.149983; c = -4;
Δ = b2-4ac
Δ = 0.1499832-4·5·(-4)
Δ = 80.022494900289
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{-(0.149983)-\sqrt{80.022494900289}}{2*5}=\frac{-0.149983-\sqrt{80.022494900289}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.149983)+\sqrt{80.022494900289}}{2*5}=\frac{-0.149983+\sqrt{80.022494900289}}{10}
$