(t+1)(t-8)=22

Solution for (t+1)(t-8)=22 equation:

(t+1)(t-8)=22

We move all terms to the left:

(t+1)(t-8)-(22)=0

We multiply parentheses ..

(+t^2-8t+t-8)-22=0

We get rid of parentheses

t^2-8t+t-8-22=0

We add all the numbers together, and all the variables

t^2-7t-30=0

a = 1; b = -7; c = -30;
Δ = b2-4ac
Δ = -72-4·1·(-30)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-13}{2*1}=\frac{-6}{2}
=-3
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+13}{2*1}=\frac{20}{2}
=10
$