200(1/2)t=675

Solution for 200(1/2)t=675 equation:

200(1/2)t=675

We move all terms to the left:

200(1/2)t-(675)=0


Domain of the equation: 2)t!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

200(+1/2)t-675=0

We multiply parentheses

200t^2-675=0

a = 200; b = 0; c = -675;
Δ = b2-4ac
Δ = 02-4·200·(-675)
Δ = 540000
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:

$\sqrt{\Delta}=\sqrt{540000}=\sqrt{90000*6}=\sqrt{90000}*\sqrt{6}=300\sqrt{6}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-300\sqrt{6}}{2*200}=\frac{0-300\sqrt{6}}{400}
=-\frac{300\sqrt{6}}{400}
=-\frac{3\sqrt{6}}{4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+300\sqrt{6}}{2*200}=\frac{0+300\sqrt{6}}{400}
=\frac{300\sqrt{6}}{400}
=\frac{3\sqrt{6}}{4}
$