100/t=4.9*t+2

Solution for 100/t=4.9*t+2 equation:

100/t=4.9t+2

We move all terms to the left:

100/t-(4.9t+2)=0


Domain of the equation: t!=0

t∈R


We get rid of parentheses

100/t-4.9t-2=0

We multiply all the terms by the denominator


-(4.9t)*t-2*t+100=0

We add all the numbers together, and all the variables

-(+4.9t)*t-2*t+100=0

We add all the numbers together, and all the variables

-2t-(+4.9t)*t+100=0

We multiply parentheses

-4t^2-2t+100=0

a = -4; b = -2; c = +100;
Δ = b2-4ac
Δ = -22-4·(-4)·100
Δ = 1604
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:

$\sqrt{\Delta}=\sqrt{1604}=\sqrt{4*401}=\sqrt{4}*\sqrt{401}=2\sqrt{401}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{401}}{2*-4}=\frac{2-2\sqrt{401}}{-8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{401}}{2*-4}=\frac{2+2\sqrt{401}}{-8}
$