81t^2=140

Solution for 81t^2=140 equation:

81t^2=140

We move all terms to the left:

81t^2-(140)=0

a = 81; b = 0; c = -140;
Δ = b2-4ac
Δ = 02-4·81·(-140)
Δ = 45360
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:

$\sqrt{\Delta}=\sqrt{45360}=\sqrt{1296*35}=\sqrt{1296}*\sqrt{35}=36\sqrt{35}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36\sqrt{35}}{2*81}=\frac{0-36\sqrt{35}}{162}
=-\frac{36\sqrt{35}}{162}
=-\frac{2\sqrt{35}}{9}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36\sqrt{35}}{2*81}=\frac{0+36\sqrt{35}}{162}
=\frac{36\sqrt{35}}{162}
=\frac{2\sqrt{35}}{9}
$