6x(1-2x)+(7-5x)+4(3x-2)=0

Solution for 6x(1-2x)+(7-5x)+4(3x-2)=0 equation:

6x(1-2x)+(7-5x)+4(3x-2)=0

We add all the numbers together, and all the variables

6x(-2x+1)+(-5x+7)+4(3x-2)=0

We multiply parentheses

-12x^2+6x+(-5x+7)+12x-8=0

We get rid of parentheses

-12x^2+6x-5x+12x+7-8=0

We add all the numbers together, and all the variables

-12x^2+13x-1=0

a = -12; b = 13; c = -1;
Δ = b2-4ac
Δ = 132-4·(-12)·(-1)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-11}{2*-12}=\frac{-24}{-24}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+11}{2*-12}=\frac{-2}{-24}
=1/12
$