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

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

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

We multiply parentheses ..

(+10x^2-14x-25x+35)=0

We get rid of parentheses

10x^2-14x-25x+35=0

We add all the numbers together, and all the variables

10x^2-39x+35=0

a = 10; b = -39; c = +35;
Δ = b2-4ac
Δ = -392-4·10·35
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-11}{2*10}=\frac{28}{20}
=1+2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+11}{2*10}=\frac{50}{20}
=2+1/2
$