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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+15x^2-35x-12x+28)=0

We get rid of parentheses

15x^2-35x-12x+28=0

We add all the numbers together, and all the variables

15x^2-47x+28=0

a = 15; b = -47; c = +28;
Δ = b2-4ac
Δ = -472-4·15·28
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-23}{2*15}=\frac{24}{30}
=4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+23}{2*15}=\frac{70}{30}
=2+1/3
$