2(2x+3)=-6x(x+9)

Solution for 2(2x+3)=-6x(x+9) equation:

2(2x+3)=-6x(x+9)

We move all terms to the left:

2(2x+3)-(-6x(x+9))=0

We multiply parentheses

4x-(-6x(x+9))+6=0


We calculate terms in parentheses: -(-6x(x+9)), so:

-6x(x+9)

We multiply parentheses

-6x^2-54x

Back to the equation:

-(-6x^2-54x)


We get rid of parentheses

6x^2+54x+4x+6=0

We add all the numbers together, and all the variables

6x^2+58x+6=0

a = 6; b = 58; c = +6;
Δ = b2-4ac
Δ = 582-4·6·6
Δ = 3220
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3220}=\sqrt{4*805}=\sqrt{4}*\sqrt{805}=2\sqrt{805}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(58)-2\sqrt{805}}{2*6}=\frac{-58-2\sqrt{805}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(58)+2\sqrt{805}}{2*6}=\frac{-58+2\sqrt{805}}{12}
$