(2x-5)(4x-7)=0

Solution for (2x-5)(4x-7)=0 equation:

(2x-5)(4x-7)=0

We multiply parentheses ..

(+8x^2-14x-20x+35)=0

We get rid of parentheses

8x^2-14x-20x+35=0

We add all the numbers together, and all the variables

8x^2-34x+35=0

a = 8; b = -34; c = +35;
Δ = b2-4ac
Δ = -342-4·8·35
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-6}{2*8}=\frac{28}{16}
=1+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+6}{2*8}=\frac{40}{16}
=2+1/2
$