(3a-4)(7a-5)=0

Solution for (3a-4)(7a-5)=0 equation:

(3a-4)(7a-5)=0

We multiply parentheses ..

(+21a^2-15a-28a+20)=0

We get rid of parentheses

21a^2-15a-28a+20=0

We add all the numbers together, and all the variables

21a^2-43a+20=0

a = 21; b = -43; c = +20;
Δ = b2-4ac
Δ = -432-4·21·20
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-43)-13}{2*21}=\frac{30}{42}
=5/7
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+13}{2*21}=\frac{56}{42}
=1+1/3
$