5x+111=(3x+27)(3x+27)

Solution for 5x+111=(3x+27)(3x+27) equation:

5x+111=(3x+27)(3x+27)

We move all terms to the left:

5x+111-((3x+27)(3x+27))=0

We multiply parentheses ..

-((+9x^2+81x+81x+729))+5x+111=0


We calculate terms in parentheses: -((+9x^2+81x+81x+729)), so:

(+9x^2+81x+81x+729)

We get rid of parentheses

9x^2+81x+81x+729

We add all the numbers together, and all the variables

9x^2+162x+729

Back to the equation:

-(9x^2+162x+729)


We add all the numbers together, and all the variables

5x-(9x^2+162x+729)+111=0

We get rid of parentheses

-9x^2+5x-162x-729+111=0

We add all the numbers together, and all the variables

-9x^2-157x-618=0

a = -9; b = -157; c = -618;
Δ = b2-4ac
Δ = -1572-4·(-9)·(-618)
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-157)-49}{2*-9}=\frac{108}{-18}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-157)+49}{2*-9}=\frac{206}{-18}
=-11+4/9
$