x^2-0.6x+0.09=0.23(0.2+x)

Solution for x^2-0.6x+0.09=0.23(0.2+x) equation:

x^2-0.6x+0.09=0.23(0.2+x)

We move all terms to the left:

x^2-0.6x+0.09-(0.23(0.2+x))=0

We add all the numbers together, and all the variables

x^2-0.6x-(0.23(x+0.2))+0.09=0


We calculate terms in parentheses: -(0.23(x+0.2)), so:

0.23(x+0.2)

We multiply parentheses

0.23x+0.046

Back to the equation:

-(0.23x+0.046)


We get rid of parentheses

x^2-0.6x-0.23x-0.046+0.09=0

We add all the numbers together, and all the variables

x^2-0.83x+0.044=0

a = 1; b = -0.83; c = +0.044;
Δ = b2-4ac
Δ = -0.832-4·1·0.044
Δ = 0.5129
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{-(-0.83)-\sqrt{0.5129}}{2*1}=\frac{0.83-\sqrt{0.5129}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.83)+\sqrt{0.5129}}{2*1}=\frac{0.83+\sqrt{0.5129}}{2}
$