(1-5a)(1-7a)=0

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

(1-5a)(1-7a)=0

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

35a^2-12a+1=0

a = 35; b = -12; c = +1;
Δ = b2-4ac
Δ = -122-4·35·1
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2}{2*35}=\frac{10}{70}
=1/7
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2}{2*35}=\frac{14}{70}
=1/5
$