n=0.5;12/n+15

Solution for n=0.5;12/n+15 equation:

n=0.512/n+15

We move all terms to the left:

n-(0.512/n+15)=0


Domain of the equation: n+15)!=0

n∈R


We get rid of parentheses

n-0.512/n-15=0

We multiply all the terms by the denominator


n*n-15*n-0.512=0

We add all the numbers together, and all the variables

-15n+n*n-0.512=0

Wy multiply elements

n^2-15n-0.512=0

a = 1; b = -15; c = -0.512;
Δ = b2-4ac
Δ = -152-4·1·(-0.512)
Δ = 227.048
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{227.048}}{2*1}=\frac{15-\sqrt{227.048}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{227.048}}{2*1}=\frac{15+\sqrt{227.048}}{2}
$