55=x(x+11)

Solution for 55=x(x+11) equation:

55=x(x+11)

We move all terms to the left:

55-(x(x+11))=0


We calculate terms in parentheses: -(x(x+11)), so:

x(x+11)

We multiply parentheses

x^2+11x

Back to the equation:

-(x^2+11x)


We get rid of parentheses

-x^2-11x+55=0

We add all the numbers together, and all the variables

-1x^2-11x+55=0

a = -1; b = -11; c = +55;
Δ = b2-4ac
Δ = -112-4·(-1)·55
Δ = 341
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{-(-11)-\sqrt{341}}{2*-1}=\frac{11-\sqrt{341}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{341}}{2*-1}=\frac{11+\sqrt{341}}{-2}
$