2x(x+2)=4(x+200)

Solution for 2x(x+2)=4(x+200) equation:

2x(x+2)=4(x+200)

We move all terms to the left:

2x(x+2)-(4(x+200))=0

We multiply parentheses

2x^2+4x-(4(x+200))=0


We calculate terms in parentheses: -(4(x+200)), so:

4(x+200)

We multiply parentheses

4x+800

Back to the equation:

-(4x+800)


We get rid of parentheses

2x^2+4x-4x-800=0

We add all the numbers together, and all the variables

2x^2-800=0

a = 2; b = 0; c = -800;
Δ = b2-4ac
Δ = 02-4·2·(-800)
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80}{2*2}=\frac{-80}{4}
=-20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80}{2*2}=\frac{80}{4}
=20
$