5.5(22.5+5.5)=x(x+5.5)

Solution for 5.5(22.5+5.5)=x(x+5.5) equation:

5.5(22.5+5.5)=x(x+5.5)

We move all terms to the left:

5.5(22.5+5.5)-(x(x+5.5))=0

We add all the numbers together, and all the variables

-(x(x+5.5))+5.528=0


We calculate terms in parentheses: -(x(x+5.5)), so:

x(x+5.5)

We multiply parentheses

x^2+5.5x

Back to the equation:

-(x^2+5.5x)


We get rid of parentheses

-x^2-5.5x+5.528=0

We add all the numbers together, and all the variables

-1x^2-5.5x+5.528=0

a = -1; b = -5.5; c = +5.528;
Δ = b2-4ac
Δ = -5.52-4·(-1)·5.528
Δ = 52.362
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{-(-5.5)-\sqrt{52.362}}{2*-1}=\frac{5.5-\sqrt{52.362}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5.5)+\sqrt{52.362}}{2*-1}=\frac{5.5+\sqrt{52.362}}{-2}
$