((0.6+x)(0.4+x))/((1-x)(0.8-x))=0

Solution for ((0.6+x)(0.4+x))/((1-x)(0.8-x))=0 equation:

((0.6+x)(0.4+x))/((1-x)(0.8-x))=0


Domain of the equation: ((1-x)(0.8-x))!=0

x∈R


We add all the numbers together, and all the variables

((x+0.6)(x+0.4))/((-1x+1)(-1x+0.8))=0

We multiply parentheses ..

((+x^2+0.4x+0.6x+0.24))/((-1x+1)(-1x+0.8))=0

We multiply all the terms by the denominator


((+x^2+0.4x+0.6x+0.24))=0


We calculate terms in parentheses: +((+x^2+0.4x+0.6x+0.24)), so:

(+x^2+0.4x+0.6x+0.24)

We get rid of parentheses

x^2+0.4x+0.6x+0.24

We add all the numbers together, and all the variables

x^2+x+0.24

Back to the equation:

+(x^2+x+0.24)


We get rid of parentheses

x^2+x+0.24=0

a = 1; b = 1; c = +0.24;
Δ = b2-4ac
Δ = 12-4·1·0.24
Δ = 0.04
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{0.04}}{2*1}=\frac{-1-\sqrt{0.04}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{0.04}}{2*1}=\frac{-1+\sqrt{0.04}}{2}
$