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

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

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

We multiply parentheses ..

(+35a^2-20a+21a-12)=0

We get rid of parentheses

35a^2-20a+21a-12=0

We add all the numbers together, and all the variables

35a^2+a-12=0

a = 35; b = 1; c = -12;
Δ = b2-4ac
Δ = 12-4·35·(-12)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-41}{2*35}=\frac{-42}{70}
=-3/5
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+41}{2*35}=\frac{40}{70}
=4/7
$