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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

3x-(2x(x-1))+12=0


We calculate terms in parentheses: -(2x(x-1)), so:

2x(x-1)

We multiply parentheses

2x^2-2x

Back to the equation:

-(2x^2-2x)


We get rid of parentheses

-2x^2+3x+2x+12=0

We add all the numbers together, and all the variables

-2x^2+5x+12=0

a = -2; b = 5; c = +12;
Δ = b2-4ac
Δ = 52-4·(-2)·12
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{-(5)-11}{2*-2}=\frac{-16}{-4}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+11}{2*-2}=\frac{6}{-4}
=-1+1/2
$