3x(3x+1)=x-6(9x-2)

Solution for 3x(3x+1)=x-6(9x-2) equation:

3x(3x+1)=x-6(9x-2)

We move all terms to the left:

3x(3x+1)-(x-6(9x-2))=0

We multiply parentheses

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


We calculate terms in parentheses: -(x-6(9x-2)), so:

x-6(9x-2)

We multiply parentheses

x-54x+12

We add all the numbers together, and all the variables

-53x+12

Back to the equation:

-(-53x+12)


We get rid of parentheses

9x^2+3x+53x-12=0

We add all the numbers together, and all the variables

9x^2+56x-12=0

a = 9; b = 56; c = -12;
Δ = b2-4ac
Δ = 562-4·9·(-12)
Δ = 3568
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:

$\sqrt{\Delta}=\sqrt{3568}=\sqrt{16*223}=\sqrt{16}*\sqrt{223}=4\sqrt{223}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-4\sqrt{223}}{2*9}=\frac{-56-4\sqrt{223}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+4\sqrt{223}}{2*9}=\frac{-56+4\sqrt{223}}{18}
$