3=x(0.035x-0.2)

Solution for 3=x(0.035x-0.2) equation:

3=x(0.035x-0.2)

We move all terms to the left:

3-(x(0.035x-0.2))=0


We calculate terms in parentheses: -(x(0.035x-0.2)), so:

x(0.035x-0.2)

We multiply parentheses

0x^2-0.2x

We add all the numbers together, and all the variables

x^2-0.2x

Back to the equation:

-(x^2-0.2x)


We get rid of parentheses

-x^2+0.2x+3=0

We add all the numbers together, and all the variables

-1x^2+0.2x+3=0

a = -1; b = 0.2; c = +3;
Δ = b2-4ac
Δ = 0.22-4·(-1)·3
Δ = 12.04
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{-(0.2)-\sqrt{12.04}}{2*-1}=\frac{-0.2-\sqrt{12.04}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.2)+\sqrt{12.04}}{2*-1}=\frac{-0.2+\sqrt{12.04}}{-2}
$