(2x-5)(5x-3)=0

Solution for (2x-5)(5x-3)=0 equation:

(2x-5)(5x-3)=0

We multiply parentheses ..

(+10x^2-6x-25x+15)=0

We get rid of parentheses

10x^2-6x-25x+15=0

We add all the numbers together, and all the variables

10x^2-31x+15=0

a = 10; b = -31; c = +15;
Δ = b2-4ac
Δ = -312-4·10·15
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-19}{2*10}=\frac{12}{20}
=3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+19}{2*10}=\frac{50}{20}
=2+1/2
$