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

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

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

We multiply parentheses ..

(+5X^2-7X-20X+28)=0

We get rid of parentheses

5X^2-7X-20X+28=0

We add all the numbers together, and all the variables

5X^2-27X+28=0

a = 5; b = -27; c = +28;
Δ = b2-4ac
Δ = -272-4·5·28
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-13}{2*5}=\frac{14}{10}
=1+2/5
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+13}{2*5}=\frac{40}{10}
=4
$