15=9.8/2*t^2

Solution for 15=9.8/2*t^2 equation:

15=9.8/2t^2

We move all terms to the left:

15-(9.8/2t^2)=0


Domain of the equation: 2t^2)!=0

t!=0/1

t!=0

t∈R


We get rid of parentheses

-9.8/2t^2+15=0

We multiply all the terms by the denominator


15*2t^2-9.8=0

Wy multiply elements

30t^2-9.8=0

a = 30; b = 0; c = -9.8;
Δ = b2-4ac
Δ = 02-4·30·(-9.8)
Δ = 1176
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:

$\sqrt{\Delta}=\sqrt{1176}=\sqrt{196*6}=\sqrt{196}*\sqrt{6}=14\sqrt{6}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{6}}{2*30}=\frac{0-14\sqrt{6}}{60}
=-\frac{14\sqrt{6}}{60}
=-\frac{7\sqrt{6}}{30}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{6}}{2*30}=\frac{0+14\sqrt{6}}{60}
=\frac{14\sqrt{6}}{60}
=\frac{7\sqrt{6}}{30}
$