X^2/0.1-x=1.8*10^-5

Solution for X^2/0.1-x=1.8*10^-5 equation:

X^2/0.1-X=1.8*10^-5

We move all terms to the left:

X^2/0.1-X-(1.8*10^-5)=0

We add all the numbers together, and all the variables

X^2/0.1-1X-5-1.8E=0

We multiply all the terms by the denominator


X^2-1X*0.1-5*0.1-(1.8E)*0.1=0

We add all the numbers together, and all the variables

X^2-1X*0.1-5*0.1-(4.8929072912263)*0.1=0

We add all the numbers together, and all the variables

X^2-1X*0.1-0.98929072912263=0

Wy multiply elements

X^2-0.1X-0.98929072912263=0

a = 1; b = -0.1; c = -0.98929072912263;
Δ = b2-4ac
Δ = -0.12-4·1·(-0.98929072912263)
Δ = 3.9671629164905
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{3.9671629164905}}{2*1}=\frac{0.1-\sqrt{3.9671629164905}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.1)+\sqrt{3.9671629164905}}{2*1}=\frac{0.1+\sqrt{3.9671629164905}}{2}
$