3x(x+4)-2(2+2x)=3(x-6x+12+2)

Solution for 3x(x+4)-2(2+2x)=3(x-6x+12+2) equation:

3x(x+4)-2(2+2x)=3(x-6x+12+2)

We move all terms to the left:

3x(x+4)-2(2+2x)-(3(x-6x+12+2))=0

We add all the numbers together, and all the variables

3x(x+4)-2(2x+2)-(3(-5x+14))=0

We multiply parentheses

3x^2+12x-4x-(3(-5x+14))-4=0


We calculate terms in parentheses: -(3(-5x+14)), so:

3(-5x+14)

We multiply parentheses

-15x+42

Back to the equation:

-(-15x+42)


We add all the numbers together, and all the variables

3x^2+8x-(-15x+42)-4=0

We get rid of parentheses

3x^2+8x+15x-42-4=0

We add all the numbers together, and all the variables

3x^2+23x-46=0

a = 3; b = 23; c = -46;
Δ = b2-4ac
Δ = 232-4·3·(-46)
Δ = 1081
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-\sqrt{1081}}{2*3}=\frac{-23-\sqrt{1081}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+\sqrt{1081}}{2*3}=\frac{-23+\sqrt{1081}}{6}
$