3t(t-4)=9

Solution for 3t(t-4)=9 equation:

3t(t-4)=9

We move all terms to the left:

3t(t-4)-(9)=0

We multiply parentheses

3t^2-12t-9=0

a = 3; b = -12; c = -9;
Δ = b2-4ac
Δ = -122-4·3·(-9)
Δ = 252
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:

$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{7}}{2*3}=\frac{12-6\sqrt{7}}{6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{7}}{2*3}=\frac{12+6\sqrt{7}}{6}
$