-4x-5=(x+9)(x+9)

Solution for -4x-5=(x+9)(x+9) equation:

-4x-5=(x+9)(x+9)

We move all terms to the left:

-4x-5-((x+9)(x+9))=0

We multiply parentheses ..

-((+x^2+9x+9x+81))-4x-5=0


We calculate terms in parentheses: -((+x^2+9x+9x+81)), so:

(+x^2+9x+9x+81)

We get rid of parentheses

x^2+9x+9x+81

We add all the numbers together, and all the variables

x^2+18x+81

Back to the equation:

-(x^2+18x+81)


We add all the numbers together, and all the variables

-4x-(x^2+18x+81)-5=0

We get rid of parentheses

-x^2-4x-18x-81-5=0

We add all the numbers together, and all the variables

-1x^2-22x-86=0

a = -1; b = -22; c = -86;
Δ = b2-4ac
Δ = -222-4·(-1)·(-86)
Δ = 140
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:

$\sqrt{\Delta}=\sqrt{140}=\sqrt{4*35}=\sqrt{4}*\sqrt{35}=2\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{35}}{2*-1}=\frac{22-2\sqrt{35}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{35}}{2*-1}=\frac{22+2\sqrt{35}}{-2}
$