5000(2)^(x/6)-1000x=0

Solution for 5000(2)^(x/6)-1000x=0 equation:

5000(2)^(x/6)-1000x=0

We add all the numbers together, and all the variables

50002^(+x/6)-1000x=0

We add all the numbers together, and all the variables

-1000x+50002^(+x/6)=0

We multiply all the terms by the denominator


-1000x*6)+50002^(+x=0

We add all the numbers together, and all the variables

x-1000x*6)+50002^(=0

Wy multiply elements

-6000x^2+x=0

a = -6000; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-6000)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-6000}=\frac{-2}{-12000}
=1/6000
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-6000}=\frac{0}{-12000}
=0
$