(x-17)(x+5)-(2x-3)(2x+3)=-67

Solution for (x-17)(x+5)-(2x-3)(2x+3)=-67 equation:

(x-17)(x+5)-(2x-3)(2x+3)=-67

We move all terms to the left:

(x-17)(x+5)-(2x-3)(2x+3)-(-67)=0

We add all the numbers together, and all the variables

(x-17)(x+5)-(2x-3)(2x+3)+67=0

We use the square of the difference formula

4x^2+(x-17)(x+5)+9+67=0

We multiply parentheses ..

4x^2+(+x^2+5x-17x-85)+9+67=0

We add all the numbers together, and all the variables

4x^2+(+x^2+5x-17x-85)+76=0

We get rid of parentheses

4x^2+x^2+5x-17x-85+76=0

We add all the numbers together, and all the variables

5x^2-12x-9=0

a = 5; b = -12; c = -9;
Δ = b2-4ac
Δ = -122-4·5·(-9)
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{-(-12)-18}{2*5}=\frac{-6}{10}
=-3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+18}{2*5}=\frac{30}{10}
=3
$