3(x-1)(2x-5)=0

Solution for 3(x-1)(2x-5)=0 equation:

3(x-1)(2x-5)=0

We multiply parentheses ..

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

We multiply parentheses

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

We add all the numbers together, and all the variables

6x^2-21x+15=0

a = 6; b = -21; c = +15;
Δ = b2-4ac
Δ = -212-4·6·15
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-9}{2*6}=\frac{12}{12}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+9}{2*6}=\frac{30}{12}
=2+1/2
$