9t(t-3)+3(3-t)=0

Solution for 9t(t-3)+3(3-t)=0 equation:

9t(t-3)+3(3-t)=0

We add all the numbers together, and all the variables

9t(t-3)+3(-1t+3)=0

We multiply parentheses

9t^2-27t-3t+9=0

We add all the numbers together, and all the variables

9t^2-30t+9=0

a = 9; b = -30; c = +9;
Δ = b2-4ac
Δ = -302-4·9·9
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-24}{2*9}=\frac{6}{18}
=1/3
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+24}{2*9}=\frac{54}{18}
=3
$