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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-3x+18x-(3(x+12)x)-9=0


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

3(x+12)x

We multiply parentheses

3x^2+36x

Back to the equation:

-(3x^2+36x)


We add all the numbers together, and all the variables

15x-(3x^2+36x)-9=0

We get rid of parentheses

-3x^2+15x-36x-9=0

We add all the numbers together, and all the variables

-3x^2-21x-9=0

a = -3; b = -21; c = -9;
Δ = b2-4ac
Δ = -212-4·(-3)·(-9)
Δ = 333
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:

$\sqrt{\Delta}=\sqrt{333}=\sqrt{9*37}=\sqrt{9}*\sqrt{37}=3\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{37}}{2*-3}=\frac{21-3\sqrt{37}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{37}}{2*-3}=\frac{21+3\sqrt{37}}{-6}
$