x^2/0.101-x=2.86*10^-3

Solution for x^2/0.101-x=2.86*10^-3 equation:

x^2/0.101-x=2.86*10^-3

We move all terms to the left:

x^2/0.101-x-(2.86*10^-3)=0

We add all the numbers together, and all the variables

x^2/0.101-1x-0.00286=0

We multiply all the terms by the denominator


x^2-1x*0.101-(0.00286)*0.101=0

We add all the numbers together, and all the variables

x^2-1x*0.101-0.00028886=0

Wy multiply elements

x^2-0.101x-0.00028886=0

a = 1; b = -0.101; c = -0.00028886;
Δ = b2-4ac
Δ = -0.1012-4·1·(-0.00028886)
Δ = 0.01135644
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{-(-0.101)-\sqrt{0.01135644}}{2*1}=\frac{0.101-\sqrt{0.01135644}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.101)+\sqrt{0.01135644}}{2*1}=\frac{0.101+\sqrt{0.01135644}}{2}
$