x^2/1.0-x=1.0*10^-5

Solution for x^2/1.0-x=1.0*10^-5 equation:

x^2/1.0-x=1.0*10^-5

We move all terms to the left:

x^2/1.0-x-(1.0*10^-5)=0

We add all the numbers together, and all the variables

x^2/1.0-1x-5-1.0E=0

We multiply all the terms by the denominator


x^2-1x*1.0-5*1.0-(1.0E)*1.0=0

We add all the numbers together, and all the variables

x^2-1x*1.0-5*1.0-(2.718281828459)*1.0=0

We add all the numbers together, and all the variables

x^2-1x*1.0-7.718281828459=0

Wy multiply elements

x^2-1x-7.718281828459=0

a = 1; b = -1; c = -7.718281828459;
Δ = b2-4ac
Δ = -12-4·1·(-7.718281828459)
Δ = 31.873127313836
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{-(-1)-\sqrt{31.873127313836}}{2*1}=\frac{1-\sqrt{31.873127313836}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{31.873127313836}}{2*1}=\frac{1+\sqrt{31.873127313836}}{2}
$