30=35t^2/2

Solution for 30=35t^2/2 equation:

30=35t^2/2

We move all terms to the left:

30-(35t^2/2)=0

We get rid of parentheses

-35t^2/2+30=0

We multiply all the terms by the denominator


-35t^2+30*2=0

We add all the numbers together, and all the variables

-35t^2+60=0

a = -35; b = 0; c = +60;
Δ = b2-4ac
Δ = 02-4·(-35)·60
Δ = 8400
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:

$\sqrt{\Delta}=\sqrt{8400}=\sqrt{400*21}=\sqrt{400}*\sqrt{21}=20\sqrt{21}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{21}}{2*-35}=\frac{0-20\sqrt{21}}{-70}
=-\frac{20\sqrt{21}}{-70}
=-\frac{2\sqrt{21}}{-7}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{21}}{2*-35}=\frac{0+20\sqrt{21}}{-70}
=\frac{20\sqrt{21}}{-70}
=\frac{2\sqrt{21}}{-7}
$