x=(-4x-3)(x-3)

Solution for x=(-4x-3)(x-3) equation:

x=(-4x-3)(x-3)

We move all terms to the left:

x-((-4x-3)(x-3))=0

We multiply parentheses ..

-((-4x^2+12x-3x+9))+x=0


We calculate terms in parentheses: -((-4x^2+12x-3x+9)), so:

(-4x^2+12x-3x+9)

We get rid of parentheses

-4x^2+12x-3x+9

We add all the numbers together, and all the variables

-4x^2+9x+9

Back to the equation:

-(-4x^2+9x+9)


We get rid of parentheses

4x^2-9x+x-9=0

We add all the numbers together, and all the variables

4x^2-8x-9=0

a = 4; b = -8; c = -9;
Δ = b2-4ac
Δ = -82-4·4·(-9)
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{13}}{2*4}=\frac{8-4\sqrt{13}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{13}}{2*4}=\frac{8+4\sqrt{13}}{8}
$