12x-4x(x-1)=2(x-2)+16

Solution for 12x-4x(x-1)=2(x-2)+16 equation:

12x-4x(x-1)=2(x-2)+16

We move all terms to the left:

12x-4x(x-1)-(2(x-2)+16)=0

We multiply parentheses

-4x^2+12x+4x-(2(x-2)+16)=0


We calculate terms in parentheses: -(2(x-2)+16), so:

2(x-2)+16

We multiply parentheses

2x-4+16

We add all the numbers together, and all the variables

2x+12

Back to the equation:

-(2x+12)


We add all the numbers together, and all the variables

-4x^2+16x-(2x+12)=0

We get rid of parentheses

-4x^2+16x-2x-12=0

We add all the numbers together, and all the variables

-4x^2+14x-12=0

a = -4; b = 14; c = -12;
Δ = b2-4ac
Δ = 142-4·(-4)·(-12)
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*-4}=\frac{-16}{-8}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2}{2*-4}=\frac{-12}{-8}
=1+1/2
$