25000/5^x*4=x

Solution for 25000/5^x*4=x equation:

25000/5^x*4=x

We move all terms to the left:

25000/5^x*4-(x)=0


Domain of the equation: 5^x*4!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+25000/5^x*4=0

We multiply all the terms by the denominator


-1x*5^x*4+25000=0

Wy multiply elements

-20x^2*4+25000=0

Wy multiply elements

-80x^2+25000=0

a = -80; b = 0; c = +25000;
Δ = b2-4ac
Δ = 02-4·(-80)·25000
Δ = 8000000
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:

$\sqrt{\Delta}=\sqrt{8000000}=\sqrt{4000000*2}=\sqrt{4000000}*\sqrt{2}=2000\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2000\sqrt{2}}{2*-80}=\frac{0-2000\sqrt{2}}{-160}
=-\frac{2000\sqrt{2}}{-160}
=-\frac{25\sqrt{2}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2000\sqrt{2}}{2*-80}=\frac{0+2000\sqrt{2}}{-160}
=\frac{2000\sqrt{2}}{-160}
=\frac{25\sqrt{2}}{-2}
$