3*2^2t=1000000

Solution for 3*2^2t=1000000 equation:

3*2^2t=1000000

We move all terms to the left:

3*2^2t-(1000000)=0

Wy multiply elements

6t^2-1000000=0

a = 6; b = 0; c = -1000000;
Δ = b2-4ac
Δ = 02-4·6·(-1000000)
Δ = 24000000
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:

$\sqrt{\Delta}=\sqrt{24000000}=\sqrt{4000000*6}=\sqrt{4000000}*\sqrt{6}=2000\sqrt{6}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2000\sqrt{6}}{2*6}=\frac{0-2000\sqrt{6}}{12}
=-\frac{2000\sqrt{6}}{12}
=-\frac{500\sqrt{6}}{3}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2000\sqrt{6}}{2*6}=\frac{0+2000\sqrt{6}}{12}
=\frac{2000\sqrt{6}}{12}
=\frac{500\sqrt{6}}{3}
$