(2x-5)(3x-10)=0

Solution for (2x-5)(3x-10)=0 equation:

(2x-5)(3x-10)=0

We multiply parentheses ..

(+6x^2-20x-15x+50)=0

We get rid of parentheses

6x^2-20x-15x+50=0

We add all the numbers together, and all the variables

6x^2-35x+50=0

a = 6; b = -35; c = +50;
Δ = b2-4ac
Δ = -352-4·6·50
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-5}{2*6}=\frac{30}{12}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+5}{2*6}=\frac{40}{12}
=3+1/3
$