44=15(t)+1/2*9.8*(t^2)

Solution for 44=15(t)+1/2*9.8*(t^2) equation:

44=15(t)+1/2*9.8(t^2)

We move all terms to the left:

44-(15(t)+1/2*9.8(t^2))=0


Domain of the equation: 2*9.8t^2)!=0

t!=0/1

t!=0

t∈R


We get rid of parentheses

-15t-1/2*9.8t^2+44=0

We multiply all the terms by the denominator


-15t*2*9.8t^2+44*2*9.8t^2-1=0

Wy multiply elements

-270t^2*9+792t*9-1=0

Wy multiply elements

-2430t^2+7128t-1=0

a = -2430; b = 7128; c = -1;
Δ = b2-4ac
Δ = 71282-4·(-2430)·(-1)
Δ = 50798664
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:

$\sqrt{\Delta}=\sqrt{50798664}=\sqrt{324*156786}=\sqrt{324}*\sqrt{156786}=18\sqrt{156786}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7128)-18\sqrt{156786}}{2*-2430}=\frac{-7128-18\sqrt{156786}}{-4860}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7128)+18\sqrt{156786}}{2*-2430}=\frac{-7128+18\sqrt{156786}}{-4860}
$