(X-7)(x+2)-20=0

Solution for (X-7)(x+2)-20=0 equation:

(X-7)(X+2)-20=0

We multiply parentheses ..

(+X^2+2X-7X-14)-20=0

We get rid of parentheses

X^2+2X-7X-14-20=0

We add all the numbers together, and all the variables

X^2-5X-34=0

a = 1; b = -5; c = -34;
Δ = b2-4ac
Δ = -52-4·1·(-34)
Δ = 161
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{-(-5)-\sqrt{161}}{2*1}=\frac{5-\sqrt{161}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{161}}{2*1}=\frac{5+\sqrt{161}}{2}
$