((x)(3.6-x))/((2.8-x)(0.4-x)=3.84

Solution for ((x)(3.6-x))/((2.8-x)(0.4-x)=3.84 equation:

((x)(3.6-x))/((2.8-x)(0.4-x)=3.84

We move all terms to the left:

((x)(3.6-x))/((2.8-x)(0.4-x)-(3.84)=0


Domain of the equation: ((2.8-x)(0.4-x)-(3.84)!=0

x∈R


We add all the numbers together, and all the variables

(x(-1x+3.6))/((-1x+2.8)(-1x+0.4)-(3.84)=0

We multiply parentheses ..

(x(-1x+3.6))/((+x^2-0.4x-2.8x+1.12)-(3.84)=0

We multiply all the terms by the denominator


(x(-1x+3.6))=0


We calculate terms in parentheses: +(x(-1x+3.6)), so:

x(-1x+3.6)

We multiply parentheses

-1x^2+3.6x

Back to the equation:

+(-1x^2+3.6x)


We get rid of parentheses

-1x^2+3.6x=0

a = -1; b = 3.6; c = 0;
Δ = b2-4ac
Δ = 3.62-4·(-1)·0
Δ = 12.96
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{-(3.6)-\sqrt{12.96}}{2*-1}=\frac{-3.6-\sqrt{12.96}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3.6)+\sqrt{12.96}}{2*-1}=\frac{-3.6+\sqrt{12.96}}{-2}
$