50=t(35+4.9t)

Solution for 50=t(35+4.9t) equation:

50=t(35+4.9t)

We move all terms to the left:

50-(t(35+4.9t))=0

We add all the numbers together, and all the variables

-(t(4.9t+35))+50=0


We calculate terms in parentheses: -(t(4.9t+35)), so:

t(4.9t+35)

We multiply parentheses

4t^2+35t

Back to the equation:

-(4t^2+35t)


We get rid of parentheses

-4t^2-35t+50=0

a = -4; b = -35; c = +50;
Δ = b2-4ac
Δ = -352-4·(-4)·50
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-45}{2*-4}=\frac{-10}{-8}
=1+1/4
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+45}{2*-4}=\frac{80}{-8}
=-10
$