(0.22x+x^2)=3.8*10^-2(0.22-x)

Solution for (0.22x+x^2)=3.8*10^-2(0.22-x) equation:

(0.22x+x^2)=3.8*10^-2(0.22-x)

We move all terms to the left:

(0.22x+x^2)-(3.8*10^-2(0.22-x))=0

We add all the numbers together, and all the variables

(0.22x+x^2)-(3.8*10^-2(-1x+0.22))=0

We get rid of parentheses

x^2+0.22x-(3.8*10^-2(-1x+0.22))=0


We calculate terms in parentheses: -(3.8*10^-2(-1x+0.22)), so:

3.8*10^-2(-1x+0.22)

determiningTheFunctionDomain
-2(-1x+0.22)+3.8*10^

We add all the numbers together, and all the variables

-2(-1x+0.22)

We multiply parentheses

2x-0.44

Back to the equation:

-(2x-0.44)


We get rid of parentheses

x^2+0.22x-2x+0.44=0

We add all the numbers together, and all the variables

x^2-1.78x+0.44=0

a = 1; b = -1.78; c = +0.44;
Δ = b2-4ac
Δ = -1.782-4·1·0.44
Δ = 1.4084
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{-(-1.78)-\sqrt{1.4084}}{2*1}=\frac{1.78-\sqrt{1.4084}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.78)+\sqrt{1.4084}}{2*1}=\frac{1.78+\sqrt{1.4084}}{2}
$