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

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

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

We multiply parentheses ..

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

We get rid of parentheses

-15x^2+12x+35x-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{-70}{-30}
=2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(47)+23}{2*-15}=\frac{-24}{-30}
=4/5
$