0=10t+9t^2

Solution for 0=10t+9t^2 equation:

0=10t+9t^2

We move all terms to the left:

0-(10t+9t^2)=0

We add all the numbers together, and all the variables

-(10t+9t^2)=0

We get rid of parentheses

-9t^2-10t=0

a = -9; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·(-9)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*-9}=\frac{0}{-18}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*-9}=\frac{20}{-18}
=-1+1/9
$