0.04=x^2/0.10-x

Solution for 0.04=x^2/0.10-x equation:

0.04=x^2/0.10-x

We move all terms to the left:

0.04-(x^2/0.10-x)=0


Domain of the equation: 0.10-x)!=0

We move all terms containing x to the left, all other terms to the right

-x)!=-0.10

x!=-0.10/1

x!=-0.10

x∈R


We get rid of parentheses

-x^2/0.10+x+0.04=0

We multiply all the terms by the denominator


-x^2+x*0.10+(0.04)*0.10=0

We add all the numbers together, and all the variables

-1x^2+x*0.10+0.004=0

Wy multiply elements

-1x^2+0.1x+0.004=0

a = -1; b = 0.1; c = +0.004;
Δ = b2-4ac
Δ = 0.12-4·(-1)·0.004
Δ = 0.026
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{0.026}}{2*-1}=\frac{-0.1-\sqrt{0.026}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.1)+\sqrt{0.026}}{2*-1}=\frac{-0.1+\sqrt{0.026}}{-2}
$