(x+1)(x-8)=3

Solution for (x+1)(x-8)=3 equation:

(x+1)(x-8)=3

We move all terms to the left:

(x+1)(x-8)-(3)=0

We multiply parentheses ..

(+x^2-8x+x-8)-3=0

We get rid of parentheses

x^2-8x+x-8-3=0

We add all the numbers together, and all the variables

x^2-7x-11=0

a = 1; b = -7; c = -11;
Δ = b2-4ac
Δ = -72-4·1·(-11)
Δ = 93
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{93}}{2*1}=\frac{7-\sqrt{93}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{93}}{2*1}=\frac{7+\sqrt{93}}{2}
$