2x+9=(2x+9)(2x+9)

Solution for 2x+9=(2x+9)(2x+9) equation:

2x+9=(2x+9)(2x+9)

We move all terms to the left:

2x+9-((2x+9)(2x+9))=0

We multiply parentheses ..

-((+4x^2+18x+18x+81))+2x+9=0


We calculate terms in parentheses: -((+4x^2+18x+18x+81)), so:

(+4x^2+18x+18x+81)

We get rid of parentheses

4x^2+18x+18x+81

We add all the numbers together, and all the variables

4x^2+36x+81

Back to the equation:

-(4x^2+36x+81)


We add all the numbers together, and all the variables

2x-(4x^2+36x+81)+9=0

We get rid of parentheses

-4x^2+2x-36x-81+9=0

We add all the numbers together, and all the variables

-4x^2-34x-72=0

a = -4; b = -34; c = -72;
Δ = b2-4ac
Δ = -342-4·(-4)·(-72)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2}{2*-4}=\frac{32}{-8}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2}{2*-4}=\frac{36}{-8}
=-4+1/2
$