-100=t(-15-4.905t)

Solution for -100=t(-15-4.905t) equation:

-100=t(-15-4.905t)

We move all terms to the left:

-100-(t(-15-4.905t))=0

We add all the numbers together, and all the variables

-(t(-4.905t-15))-100=0


We calculate terms in parentheses: -(t(-4.905t-15)), so:

t(-4.905t-15)

We multiply parentheses

-4t^2-15t

Back to the equation:

-(-4t^2-15t)


We get rid of parentheses

4t^2+15t-100=0

a = 4; b = 15; c = -100;
Δ = b2-4ac
Δ = 152-4·4·(-100)
Δ = 1825
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:

$\sqrt{\Delta}=\sqrt{1825}=\sqrt{25*73}=\sqrt{25}*\sqrt{73}=5\sqrt{73}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-5\sqrt{73}}{2*4}=\frac{-15-5\sqrt{73}}{8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+5\sqrt{73}}{2*4}=\frac{-15+5\sqrt{73}}{8}
$