15=1/2*10*t2

Solution for 15=1/2*10*t2 equation:

15=1/2*10t^2

We move all terms to the left:

15-(1/2*10t^2)=0


Domain of the equation: 2*10t^2)!=0

t!=0/1

t!=0

t∈R


We get rid of parentheses

-1/2*10t^2+15=0

We multiply all the terms by the denominator


15*2*10t^2-1=0

Wy multiply elements

300t^2*1-1=0

Wy multiply elements

300t^2-1=0

a = 300; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·300·(-1)
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{3}}{2*300}=\frac{0-20\sqrt{3}}{600}
=-\frac{20\sqrt{3}}{600}
=-\frac{\sqrt{3}}{30}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{3}}{2*300}=\frac{0+20\sqrt{3}}{600}
=\frac{20\sqrt{3}}{600}
=\frac{\sqrt{3}}{30}
$