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

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

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

We multiply parentheses ..

(+20x^2-28x-25x+35)=0

We get rid of parentheses

20x^2-28x-25x+35=0

We add all the numbers together, and all the variables

20x^2-53x+35=0

a = 20; b = -53; c = +35;
Δ = b2-4ac
Δ = -532-4·20·35
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-53)-3}{2*20}=\frac{50}{40}
=1+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+3}{2*20}=\frac{56}{40}
=1+2/5
$