4000=2000x(1.12^X)

Solution for 4000=2000x(1.12^X) equation:

4000=2000x(1.12^x)

We move all terms to the left:

4000-(2000x(1.12^x))=0


We calculate terms in parentheses: -(2000x(1.12^x)), so:

2000x(1.12^x)

We multiply parentheses

2000x^2

Back to the equation:

-(2000x^2)


a = -2000; b = 0; c = +4000;
Δ = b2-4ac
Δ = 02-4·(-2000)·4000
Δ = 32000000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{32000000}=\sqrt{16000000*2}=\sqrt{16000000}*\sqrt{2}=4000\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4000\sqrt{2}}{2*-2000}=\frac{0-4000\sqrt{2}}{-4000}
=-\frac{4000\sqrt{2}}{-4000}
=-\frac{\sqrt{2}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4000\sqrt{2}}{2*-2000}=\frac{0+4000\sqrt{2}}{-4000}
=\frac{4000\sqrt{2}}{-4000}
=\frac{\sqrt{2}}{-1}
$