.5=5t^2

Solution for .5=5t^2 equation:

.5=5t^2

We move all terms to the left:

.5-(5t^2)=0

We add all the numbers together, and all the variables

-5t^2+0.5=0

a = -5; b = 0; c = +0.5;
Δ = b2-4ac
Δ = 02-4·(-5)·0.5
Δ = 10
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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