100/4.9=t^2+10t

Solution for 100/4.9=t^2+10t equation:

100/4.9=t^2+10t

We move all terms to the left:

100/4.9-(t^2+10t)=0

We get rid of parentheses

-t^2-10t+100/4.9=0

We multiply all the terms by the denominator


-t^2*4.9-10t*4.9+100=0

Wy multiply elements

-4.9t^2-49t+100=0

a = -4.9; b = -49; c = +100;
Δ = b2-4ac
Δ = -492-4·(-4.9)·100
Δ = 4361
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:

$\sqrt{\Delta}=\sqrt{4361}=\sqrt{49*89}=\sqrt{49}*\sqrt{89}=7\sqrt{89}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-49)-7\sqrt{89}}{2*-4.9}=\frac{49-7\sqrt{89}}{-9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49)+7\sqrt{89}}{2*-4.9}=\frac{49+7\sqrt{89}}{-9.8}
$