(0.1-x)/x^2=4

Solution for (0.1-x)/x^2=4 equation:

(0.1-x)/x^2=4

We move all terms to the left:

(0.1-x)/x^2-(4)=0


Domain of the equation: x^2!=0

x^2!=0/

x^2!=√0

x!=0

x∈R


We add all the numbers together, and all the variables

(-1x+0.1)/x^2-4=0

We multiply all the terms by the denominator


(-1x+0.1)-4*x^2=0

We add all the numbers together, and all the variables

-4x^2+(-1x+0.1)=0

We get rid of parentheses

-4x^2-1x+0.1=0

a = -4; b = -1; c = +0.1;
Δ = b2-4ac
Δ = -12-4·(-4)·0.1
Δ = 2.6
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{2.6}}{2*-4}=\frac{1-\sqrt{2.6}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{2.6}}{2*-4}=\frac{1+\sqrt{2.6}}{-8}
$