25=(-4.9t^2+25t)/t

Solution for 25=(-4.9t^2+25t)/t equation:

25=(-4.9t^2+25t)/t

We move all terms to the left:

25-((-4.9t^2+25t)/t)=0


Domain of the equation: t)!=0

t!=0/1

t!=0

t∈R


We multiply all the terms by the denominator


-((-4.9t^2+25t)+25*t)=0


We calculate terms in parentheses: -((-4.9t^2+25t)+25*t), so:

(-4.9t^2+25t)+25*t

We add all the numbers together, and all the variables

(-4.9t^2+25t)+25t

We get rid of parentheses

-4.9t^2+25t+25t

We add all the numbers together, and all the variables

-4.9t^2+50t

Back to the equation:

-(-4.9t^2+50t)


We get rid of parentheses

4.9t^2-50t=0

a = 4.9; b = -50; c = 0;
Δ = b2-4ac
Δ = -502-4·4.9·0
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-50}{2*4.9}=\frac{0}{9.8}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+50}{2*4.9}=\frac{100}{9.8}
=10+2/9.8
$