142=5t2

Solution for 142=5t2 equation:

142=5t^2

We move all terms to the left:

142-(5t^2)=0

a = -5; b = 0; c = +142;
Δ = b2-4ac
Δ = 02-4·(-5)·142
Δ = 2840
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:

$\sqrt{\Delta}=\sqrt{2840}=\sqrt{4*710}=\sqrt{4}*\sqrt{710}=2\sqrt{710}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{710}}{2*-5}=\frac{0-2\sqrt{710}}{-10}
=-\frac{2\sqrt{710}}{-10}
=-\frac{\sqrt{710}}{-5}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{710}}{2*-5}=\frac{0+2\sqrt{710}}{-10}
=\frac{2\sqrt{710}}{-10}
=\frac{\sqrt{710}}{-5}
$