x=0.06/x+0.1

Solution for x=0.06/x+0.1 equation:

x=0.06/x+0.1

We move all terms to the left:

x-(0.06/x+0.1)=0


Domain of the equation: x+0.1)!=0

x∈R


We get rid of parentheses

x-0.06/x-0.1=0

We multiply all the terms by the denominator


x*x-(0.1)*x-0.06=0

We multiply parentheses

x*x-0.1x-0.06=0

Wy multiply elements

x^2-0.1x-0.06=0

a = 1; b = -0.1; c = -0.06;
Δ = b2-4ac
Δ = -0.12-4·1·(-0.06)
Δ = 0.25
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{-(-0.1)-\sqrt{0.25}}{2*1}=\frac{0.1-\sqrt{0.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.1)+\sqrt{0.25}}{2*1}=\frac{0.1+\sqrt{0.25}}{2}
$