(x-17)(7x+5)=0

Solution for (x-17)(7x+5)=0 equation:

(x-17)(7x+5)=0

We multiply parentheses ..

(+7x^2+5x-119x-85)=0

We get rid of parentheses

7x^2+5x-119x-85=0

We add all the numbers together, and all the variables

7x^2-114x-85=0

a = 7; b = -114; c = -85;
Δ = b2-4ac
Δ = -1142-4·7·(-85)
Δ = 15376
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15376}=124$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-114)-124}{2*7}=\frac{-10}{14}
=-5/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-114)+124}{2*7}=\frac{238}{14}
=17
$