8t2=16106

Solution for 8t2=16106 equation:

8t^2=16106

We move all terms to the left:

8t^2-(16106)=0

a = 8; b = 0; c = -16106;
Δ = b2-4ac
Δ = 02-4·8·(-16106)
Δ = 515392
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:

$\sqrt{\Delta}=\sqrt{515392}=\sqrt{64*8053}=\sqrt{64}*\sqrt{8053}=8\sqrt{8053}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{8053}}{2*8}=\frac{0-8\sqrt{8053}}{16}
=-\frac{8\sqrt{8053}}{16}
=-\frac{\sqrt{8053}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{8053}}{2*8}=\frac{0+8\sqrt{8053}}{16}
=\frac{8\sqrt{8053}}{16}
=\frac{\sqrt{8053}}{2}
$