.15/x+.2=x

Solution for .15/x+.2=x equation:

.15/x+.2=x

We move all terms to the left:

.15/x+.2-(x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-1x+.15/x+0.2=0

We multiply all the terms by the denominator


-1x*x+(0.2)*x+.15=0

We add all the numbers together, and all the variables

-1x*x+(0.2)*x+0.15=0

We multiply parentheses

-1x*x+0.2x+0.15=0

Wy multiply elements

-1x^2+0.2x+0.15=0

a = -1; b = 0.2; c = +0.15;
Δ = b2-4ac
Δ = 0.22-4·(-1)·0.15
Δ = 0.64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0.2)-\sqrt{0.64}}{2*-1}=\frac{-0.2-\sqrt{0.64}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.2)+\sqrt{0.64}}{2*-1}=\frac{-0.2+\sqrt{0.64}}{-2}
$