-(x-11)(x+3)=(x)

Solution for -(x-11)(x+3)=(x) equation:

-(x-11)(x+3)=(x)

We move all terms to the left:

-(x-11)(x+3)-((x))=0

determiningTheFunctionDomain
-(x-11)(x+3)-x=0

We add all the numbers together, and all the variables

-1x-(x-11)(x+3)=0

We multiply parentheses ..

-(+x^2+3x-11x-33)-1x=0

We get rid of parentheses

-x^2-3x+11x-1x+33=0

We add all the numbers together, and all the variables

-1x^2+7x+33=0

a = -1; b = 7; c = +33;
Δ = b2-4ac
Δ = 72-4·(-1)·33
Δ = 181
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{181}}{2*-1}=\frac{-7-\sqrt{181}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{181}}{2*-1}=\frac{-7+\sqrt{181}}{-2}
$