(t-8)(t-9)=0

Solution for (t-8)(t-9)=0 equation:

(t-8)(t-9)=0

We multiply parentheses ..

(+t^2-9t-8t+72)=0

We get rid of parentheses

t^2-9t-8t+72=0

We add all the numbers together, and all the variables

t^2-17t+72=0

a = 1; b = -17; c = +72;
Δ = b2-4ac
Δ = -172-4·1·72
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-1}{2*1}=\frac{16}{2}
=8
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+1}{2*1}=\frac{18}{2}
=9
$