x^2/0.1-x=10^-5

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

x^2/0.1-x=10^-5

We move all terms to the left:

x^2/0.1-x-(10^-5)=0

We add all the numbers together, and all the variables

x^2/0.1-1x-5-1.0E=0

We multiply all the terms by the denominator


x^2-1x*0.1-5*0.1-(1.0E)*0.1=0

We add all the numbers together, and all the variables

x^2-1x*0.1-5*0.1-(2.71828182846)*0.1=0

We add all the numbers together, and all the variables

x^2-1x*0.1-0.771828182846=0

Wy multiply elements

x^2-0.1x-0.771828182846=0

a = 1; b = -0.1; c = -0.771828182846;
Δ = b2-4ac
Δ = -0.12-4·1·(-0.771828182846)
Δ = 3.09731273138
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{3.09731273138}}{2*1}=\frac{0.1-\sqrt{3.09731273138}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.1)+\sqrt{3.09731273138}}{2*1}=\frac{0.1+\sqrt{3.09731273138}}{2}
$