6x+2x(3x+6)=4x+9(x+6)

Solution for 6x+2x(3x+6)=4x+9(x+6) equation:

6x+2x(3x+6)=4x+9(x+6)

We move all terms to the left:

6x+2x(3x+6)-(4x+9(x+6))=0

We multiply parentheses

6x^2+6x+12x-(4x+9(x+6))=0


We calculate terms in parentheses: -(4x+9(x+6)), so:

4x+9(x+6)

We multiply parentheses

4x+9x+54

We add all the numbers together, and all the variables

13x+54

Back to the equation:

-(13x+54)


We add all the numbers together, and all the variables

6x^2+18x-(13x+54)=0

We get rid of parentheses

6x^2+18x-13x-54=0

We add all the numbers together, and all the variables

6x^2+5x-54=0

a = 6; b = 5; c = -54;
Δ = b2-4ac
Δ = 52-4·6·(-54)
Δ = 1321
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{-(5)-\sqrt{1321}}{2*6}=\frac{-5-\sqrt{1321}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{1321}}{2*6}=\frac{-5+\sqrt{1321}}{12}
$