-(x+6)(x+4)=x(x+11+16)

Solution for -(x+6)(x+4)=x(x+11+16) equation:

-(x+6)(x+4)=x(x+11+16)

We move all terms to the left:

-(x+6)(x+4)-(x(x+11+16))=0

We add all the numbers together, and all the variables

-(x+6)(x+4)-(x(x+27))=0

We multiply parentheses ..

-(+x^2+4x+6x+24)-(x(x+27))=0


We calculate terms in parentheses: -(x(x+27)), so:

x(x+27)

We multiply parentheses

x^2+27x

Back to the equation:

-(x^2+27x)


We get rid of parentheses

-x^2-x^2-4x-6x-27x-24=0

We add all the numbers together, and all the variables

-2x^2-37x-24=0

a = -2; b = -37; c = -24;
Δ = b2-4ac
Δ = -372-4·(-2)·(-24)
Δ = 1177
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{-(-37)-\sqrt{1177}}{2*-2}=\frac{37-\sqrt{1177}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+\sqrt{1177}}{2*-2}=\frac{37+\sqrt{1177}}{-4}
$