(5x-7)(7x-4)=0

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

(5x-7)(7x-4)=0

We multiply parentheses ..

(+35x^2-20x-49x+28)=0

We get rid of parentheses

35x^2-20x-49x+28=0

We add all the numbers together, and all the variables

35x^2-69x+28=0

a = 35; b = -69; c = +28;
Δ = b2-4ac
Δ = -692-4·35·28
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-69)-29}{2*35}=\frac{40}{70}
=4/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-69)+29}{2*35}=\frac{98}{70}
=1+2/5
$