x=(0.02+x)(2x)

Solution for x=(0.02+x)(2x) equation:

x=(0.02+x)(2x)

We move all terms to the left:

x-((0.02+x)(2x))=0

We add all the numbers together, and all the variables

x-((x+0.02)2x)=0


We calculate terms in parentheses: -((x+0.02)2x), so:

(x+0.02)2x

We multiply parentheses

2x^2+0.04x

Back to the equation:

-(2x^2+0.04x)


We get rid of parentheses

-2x^2+x-0.04x=0

We add all the numbers together, and all the variables

-2x^2+0.96x=0

a = -2; b = 0.96; c = 0;
Δ = b2-4ac
Δ = 0.962-4·(-2)·0
Δ = 0.9216
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{-(0.96)-\sqrt{0.9216}}{2*-2}=\frac{-0.96-\sqrt{0.9216}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.96)+\sqrt{0.9216}}{2*-2}=\frac{-0.96+\sqrt{0.9216}}{-4}
$