9(2x-1)3x=3(12+x)

Solution for 9(2x-1)3x=3(12+x) equation:

9(2x-1)3x=3(12+x)

We move all terms to the left:

9(2x-1)3x-(3(12+x))=0

We add all the numbers together, and all the variables

9(2x-1)3x-(3(x+12))=0

We multiply parentheses

54x^2-27x-(3(x+12))=0


We calculate terms in parentheses: -(3(x+12)), so:

3(x+12)

We multiply parentheses

3x+36

Back to the equation:

-(3x+36)


We get rid of parentheses

54x^2-27x-3x-36=0

We add all the numbers together, and all the variables

54x^2-30x-36=0

a = 54; b = -30; c = -36;
Δ = b2-4ac
Δ = -302-4·54·(-36)
Δ = 8676
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:

$\sqrt{\Delta}=\sqrt{8676}=\sqrt{36*241}=\sqrt{36}*\sqrt{241}=6\sqrt{241}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{241}}{2*54}=\frac{30-6\sqrt{241}}{108}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{241}}{2*54}=\frac{30+6\sqrt{241}}{108}
$