0.069=x-(0.65*(x^2))

Solution for 0.069=x-(0.65*(x^2)) equation:

0.069=x-(0.65(x^2))

We move all terms to the left:

0.069-(x-(0.65(x^2)))=0


We calculate terms in parentheses: -(x-(0.65x^2)), so:

x-(0.65x^2)

We get rid of parentheses

-0.65x^2+x

Back to the equation:

-(-0.65x^2+x)


We get rid of parentheses

0.65x^2-x+0.069=0

We add all the numbers together, and all the variables

0.65x^2-1x+0.069=0

a = 0.65; b = -1; c = +0.069;
Δ = b2-4ac
Δ = -12-4·0.65·0.069
Δ = 0.8206
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)-\sqrt{0.8206}}{2*0.65}=\frac{1-\sqrt{0.8206}}{1.3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{0.8206}}{2*0.65}=\frac{1+\sqrt{0.8206}}{1.3}
$