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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

6x^2-25x+25=0

a = 6; b = -25; c = +25;
Δ = b2-4ac
Δ = -252-4·6·25
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{-(-25)-5}{2*6}=\frac{20}{12}
=1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+5}{2*6}=\frac{30}{12}
=2+1/2
$