(0.1+x)(0.1+x)=(0.5-x)

Solution for (0.1+x)(0.1+x)=(0.5-x) equation:

(0.1+x)(0.1+x)=(0.5-x)

We move all terms to the left:

(0.1+x)(0.1+x)-((0.5-x))=0

We add all the numbers together, and all the variables

(x+0.1)(x+0.1)-((-1x+0.5))=0

We multiply parentheses ..

(+x^2+0.1x+0.1x+0.01)-((-1x+0.5))=0


We calculate terms in parentheses: -((-1x+0.5)), so:

(-1x+0.5)

We get rid of parentheses

-1x+0.5

Back to the equation:

-(-1x+0.5)


We get rid of parentheses

x^2+0.1x+0.1x+1x+0.01-0.5=0

We add all the numbers together, and all the variables

x^2+1.2x-0.49=0

a = 1; b = 1.2; c = -0.49;
Δ = b2-4ac
Δ = 1.22-4·1·(-0.49)
Δ = 3.4
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{-(1.2)-\sqrt{3.4}}{2*1}=\frac{-1.2-\sqrt{3.4}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.2)+\sqrt{3.4}}{2*1}=\frac{-1.2+\sqrt{3.4}}{2}
$