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

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

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

We multiply parentheses ..

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

We multiply parentheses

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

We add all the numbers together, and all the variables

6x^2-16x+10=0

a = 6; b = -16; c = +10;
Δ = b2-4ac
Δ = -162-4·6·10
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4}{2*6}=\frac{12}{12}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4}{2*6}=\frac{20}{12}
=1+2/3
$