-2(3x-4)(x-1)=0

Solution for -2(3x-4)(x-1)=0 equation:

-2(3x-4)(x-1)=0

We multiply parentheses ..

-2(+3x^2-3x-4x+4)=0

We multiply parentheses

-6x^2+6x+8x-8=0

We add all the numbers together, and all the variables

-6x^2+14x-8=0

a = -6; b = 14; c = -8;
Δ = b2-4ac
Δ = 142-4·(-6)·(-8)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2}{2*-6}=\frac{-16}{-12}
=1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2}{2*-6}=\frac{-12}{-12}
=1
$