4=(0.4+x)(.25-x)/(0.1-x)(0.1-x)

Solution for 4=(0.4+x)(.25-x)/(0.1-x)(0.1-x) equation:

4=(0.4+x)(.25-x)/(0.1-x)(0.1-x)

We move all terms to the left:

4-((0.4+x)(.25-x)/(0.1-x)(0.1-x))=0


Domain of the equation: (0.1-x)(0.1-x))!=0

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

-x)(0.1-x)!=-0.1

x∈R


We add all the numbers together, and all the variables

-((x+0.4)(-1x+0.25)/(-1x+0.1)(-1x+0.1))+4=0

We multiply parentheses ..

-((-1x^2+0.25x-0.4x+0.1)/(-1x+0.1)(-1x+0.1))+4=0

We multiply all the terms by the denominator


-((-1x^2+0.25x-0.4x+0.1)+4*(-1x+0.1)(-1x+0.1))=0


We calculate terms in parentheses: -((-1x^2+0.25x-0.4x+0.1)+4*(-1x+0.1)(-1x+0.1)), so:

(-1x^2+0.25x-0.4x+0.1)+4*(-1x+0.1)(-1x+0.1)

We get rid of parentheses

-1x^2+0.25x-0.4x+4*(-1x+0.1)(-1x+0.1)+0.1

We multiply parentheses ..

-1x^2+4*(+x^2-0.1x-0.1x+0.01)+0.25x-0.4x+0.1

We add all the numbers together, and all the variables

-1x^2+4*(+x^2-0.1x-0.1x+0.01)-0.15x+0.1

We multiply parentheses

-1x^2+4x^2+0x+0x-0.15x+0.04+0.1

We add all the numbers together, and all the variables

3x^2+1.85x+0.14

Back to the equation:

-(3x^2+1.85x+0.14)


We get rid of parentheses

-3x^2-1.85x-0.14=0

a = -3; b = -1.85; c = -0.14;
Δ = b2-4ac
Δ = -1.852-4·(-3)·(-0.14)
Δ = 1.7425
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{-(-1.85)-\sqrt{1.7425}}{2*-3}=\frac{1.85-\sqrt{1.7425}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.85)+\sqrt{1.7425}}{2*-3}=\frac{1.85+\sqrt{1.7425}}{-6}
$