0.11=(x+0.5)x

Solution for 0.11=(x+0.5)x equation:

0.11=(x+0.5)x

We move all terms to the left:

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


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

(x+0.5)x

We multiply parentheses

x^2+0.5x

Back to the equation:

-(x^2+0.5x)


We get rid of parentheses

-x^2-0.5x+0.11=0

We add all the numbers together, and all the variables

-1x^2-0.5x+0.11=0

a = -1; b = -0.5; c = +0.11;
Δ = b2-4ac
Δ = -0.52-4·(-1)·0.11
Δ = 0.69
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{-(-0.5)-\sqrt{0.69}}{2*-1}=\frac{0.5-\sqrt{0.69}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.5)+\sqrt{0.69}}{2*-1}=\frac{0.5+\sqrt{0.69}}{-2}
$