4400.00=4000.00(1+r(2))

Solution for 4400.00=4000.00(1+r(2)) equation:

4400.00=4000.00(1+r(2))

We move all terms to the left:

4400.00-(4000.00(1+r(2)))=0

We add all the numbers together, and all the variables

-(4000.00(+r^2+1))+4400.00=0

We add all the numbers together, and all the variables

-(4000.00(+r^2+1))+4400=0


We calculate terms in parentheses: -(4000.00(+r^2+1)), so:

4000.00(+r^2+1)

We multiply parentheses

4000r^2+4000

Back to the equation:

-(4000r^2+4000)


We get rid of parentheses

-4000r^2-4000+4400=0

We add all the numbers together, and all the variables

-4000r^2+400=0

a = -4000; b = 0; c = +400;
Δ = b2-4ac
Δ = 02-4·(-4000)·400
Δ = 6400000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6400000}=\sqrt{640000*10}=\sqrt{640000}*\sqrt{10}=800\sqrt{10}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-800\sqrt{10}}{2*-4000}=\frac{0-800\sqrt{10}}{-8000}
=-\frac{800\sqrt{10}}{-8000}
=-\frac{\sqrt{10}}{-10}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+800\sqrt{10}}{2*-4000}=\frac{0+800\sqrt{10}}{-8000}
=\frac{800\sqrt{10}}{-8000}
=\frac{\sqrt{10}}{-10}
$