3(x+9)=2(3x+27)x=

Solution for 3(x+9)=2(3x+27)x= equation:

3(x+9)=2(3x+27)x=

We move all terms to the left:

3(x+9)-(2(3x+27)x)=0

We multiply parentheses

3x-(2(3x+27)x)+27=0


We calculate terms in parentheses: -(2(3x+27)x), so:

2(3x+27)x

We multiply parentheses

6x^2+54x

Back to the equation:

-(6x^2+54x)


We get rid of parentheses

-6x^2+3x-54x+27=0

We add all the numbers together, and all the variables

-6x^2-51x+27=0

a = -6; b = -51; c = +27;
Δ = b2-4ac
Δ = -512-4·(-6)·27
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-57}{2*-6}=\frac{-6}{-12}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+57}{2*-6}=\frac{108}{-12}
=-9
$