50000x*1.04^x=650000

Solution for 50000x*1.04^x=650000 equation:

50000x*1.04^x=650000

We move all terms to the left:

50000x*1.04^x-(650000)=0

Wy multiply elements

50000x^2-650000=0

a = 50000; b = 0; c = -650000;
Δ = b2-4ac
Δ = 02-4·50000·(-650000)
Δ = 130000000000
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:

$\sqrt{\Delta}=\sqrt{130000000000}=\sqrt{10000000000*13}=\sqrt{10000000000}*\sqrt{13}=100000\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-100000\sqrt{13}}{2*50000}=\frac{0-100000\sqrt{13}}{100000}
=-\frac{100000\sqrt{13}}{100000}
=-\sqrt{13}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+100000\sqrt{13}}{2*50000}=\frac{0+100000\sqrt{13}}{100000}
=\frac{100000\sqrt{13}}{100000}
=\sqrt{13}
$