(2x-17)*(x-5)-(3x+1)*(x-7)=84

Solution for (2x-17)*(x-5)-(3x+1)*(x-7)=84 equation:

(2x-17)(x-5)-(3x+1)(x-7)=84

We move all terms to the left:

(2x-17)(x-5)-(3x+1)(x-7)-(84)=0

We multiply parentheses ..

(+2x^2-10x-17x+85)-(3x+1)(x-7)-84=0

We get rid of parentheses

2x^2-10x-17x-(3x+1)(x-7)+85-84=0

We multiply parentheses ..

2x^2-(+3x^2-21x+x-7)-10x-17x+85-84=0

We add all the numbers together, and all the variables

2x^2-(+3x^2-21x+x-7)-27x+1=0

We get rid of parentheses

2x^2-3x^2+21x-x-27x+7+1=0

We add all the numbers together, and all the variables

-1x^2-7x+8=0

a = -1; b = -7; c = +8;
Δ = b2-4ac
Δ = -72-4·(-1)·8
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-9}{2*-1}=\frac{-2}{-2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+9}{2*-1}=\frac{16}{-2}
=-8
$