2(t-3)(t-3)-72=0

Solution for 2(t-3)(t-3)-72=0 equation:

2(t-3)(t-3)-72=0

We multiply parentheses ..

2(+t^2-3t-3t+9)-72=0

We multiply parentheses

2t^2-6t-6t+18-72=0

We add all the numbers together, and all the variables

2t^2-12t-54=0

a = 2; b = -12; c = -54;
Δ = b2-4ac
Δ = -122-4·2·(-54)
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{-(-12)-24}{2*2}=\frac{-12}{4}
=-3
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+24}{2*2}=\frac{36}{4}
=9
$