7.5=2t^2

Solution for 7.5=2t^2 equation:

7.5=2t^2

We move all terms to the left:

7.5-(2t^2)=0

a = -2; b = 0; c = +7.5;
Δ = b2-4ac
Δ = 02-4·(-2)·7.5
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{15}}{2*-2}=\frac{0-2\sqrt{15}}{-4}
=-\frac{2\sqrt{15}}{-4}
=-\frac{\sqrt{15}}{-2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{15}}{2*-2}=\frac{0+2\sqrt{15}}{-4}
=\frac{2\sqrt{15}}{-4}
=\frac{\sqrt{15}}{-2}
$