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

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

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

We multiply parentheses ..

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

We multiply parentheses

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

We add all the numbers together, and all the variables

15x^2-21x+6=0

a = 15; b = -21; c = +6;
Δ = b2-4ac
Δ = -212-4·15·6
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*15}=\frac{12}{30}
=2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+9}{2*15}=\frac{30}{30}
=1
$