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

Solution for (3x+5)(x-2)-(x-2)(x+17)=0 equation:

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

We multiply parentheses ..

(+3x^2-6x+5x-10)-(x-2)(x+17)=0

We get rid of parentheses

3x^2-6x+5x-(x-2)(x+17)-10=0

We multiply parentheses ..

3x^2-(+x^2+17x-2x-34)-6x+5x-10=0

We add all the numbers together, and all the variables

3x^2-(+x^2+17x-2x-34)-1x-10=0

We get rid of parentheses

3x^2-x^2-17x+2x-1x+34-10=0

We add all the numbers together, and all the variables

2x^2-16x+24=0

a = 2; b = -16; c = +24;
Δ = b2-4ac
Δ = -162-4·2·24
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8}{2*2}=\frac{8}{4}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8}{2*2}=\frac{24}{4}
=6
$