(1/2)10t=50,000

Solution for (1/2)10t=50,000 equation:

(1/2)10t=50.000

We move all terms to the left:

(1/2)10t-(50.000)=0


Domain of the equation: 2)10t!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

(+1/2)10t-50=0

We multiply parentheses

10t^2-50=0

a = 10; b = 0; c = -50;
Δ = b2-4ac
Δ = 02-4·10·(-50)
Δ = 2000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2000}=\sqrt{400*5}=\sqrt{400}*\sqrt{5}=20\sqrt{5}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{5}}{2*10}=\frac{0-20\sqrt{5}}{20}
=-\frac{20\sqrt{5}}{20}
=-\sqrt{5}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{5}}{2*10}=\frac{0+20\sqrt{5}}{20}
=\frac{20\sqrt{5}}{20}
=\sqrt{5}
$