(x+9)=(6x2-3x-3)

Solution for (x+9)=(6x2-3x-3) equation:

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

We move all terms to the left:

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

We get rid of parentheses

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


We calculate terms in parentheses: -((6x^2-3x-3)), so:

(6x^2-3x-3)

We get rid of parentheses

6x^2-3x-3

Back to the equation:

-(6x^2-3x-3)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-6x^2+4x+12=0

a = -6; b = 4; c = +12;
Δ = b2-4ac
Δ = 42-4·(-6)·12
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{19}}{2*-6}=\frac{-4-4\sqrt{19}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{19}}{2*-6}=\frac{-4+4\sqrt{19}}{-12}
$