5t2=142

Solution for 5t2=142 equation:

5t^2=142

We move all terms to the left:

5t^2-(142)=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}
$