(x+7)(x-9)=17

Solution for (x+7)(x-9)=17 equation:

(x+7)(x-9)=17

We move all terms to the left:

(x+7)(x-9)-(17)=0

We multiply parentheses ..

(+x^2-9x+7x-63)-17=0

We get rid of parentheses

x^2-9x+7x-63-17=0

We add all the numbers together, and all the variables

x^2-2x-80=0

a = 1; b = -2; c = -80;
Δ = b2-4ac
Δ = -22-4·1·(-80)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-18}{2*1}=\frac{-16}{2}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+18}{2*1}=\frac{20}{2}
=10
$