5000x*1,08^x=1000000

Solution for 5000x*1,08^x=1000000 equation:

5000x*1.08^x=1000000

We move all terms to the left:

5000x*1.08^x-(1000000)=0

Wy multiply elements

5000x^2-1000000=0

a = 5000; b = 0; c = -1000000;
Δ = b2-4ac
Δ = 02-4·5000·(-1000000)
Δ = 20000000000
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:

$\sqrt{\Delta}=\sqrt{20000000000}=\sqrt{10000000000*2}=\sqrt{10000000000}*\sqrt{2}=100000\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-100000\sqrt{2}}{2*5000}=\frac{0-100000\sqrt{2}}{10000}
=-\frac{100000\sqrt{2}}{10000}
=-10\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+100000\sqrt{2}}{2*5000}=\frac{0+100000\sqrt{2}}{10000}
=\frac{100000\sqrt{2}}{10000}
=10\sqrt{2}
$