2x(x+6)=4(3x+18)

Solution for 2x(x+6)=4(3x+18) equation:

2x(x+6)=4(3x+18)

We move all terms to the left:

2x(x+6)-(4(3x+18))=0

We multiply parentheses

2x^2+12x-(4(3x+18))=0


We calculate terms in parentheses: -(4(3x+18)), so:

4(3x+18)

We multiply parentheses

12x+72

Back to the equation:

-(12x+72)


We get rid of parentheses

2x^2+12x-12x-72=0

We add all the numbers together, and all the variables

2x^2-72=0

a = 2; b = 0; c = -72;
Δ = b2-4ac
Δ = 02-4·2·(-72)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24}{2*2}=\frac{-24}{4}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*2}=\frac{24}{4}
=6
$