(7x+1)(5x-1)=0

Solution for (7x+1)(5x-1)=0 equation:

(7x+1)(5x-1)=0

We multiply parentheses ..

(+35x^2-7x+5x-1)=0

We get rid of parentheses

35x^2-7x+5x-1=0

We add all the numbers together, and all the variables

35x^2-2x-1=0

a = 35; b = -2; c = -1;
Δ = b2-4ac
Δ = -22-4·35·(-1)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-12}{2*35}=\frac{-10}{70}
=-1/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+12}{2*35}=\frac{14}{70}
=1/5
$