11x(x+1)=55

Solution for 11x(x+1)=55 equation:

11x(x+1)=55

We move all terms to the left:

11x(x+1)-(55)=0

We multiply parentheses

11x^2+11x-55=0

a = 11; b = 11; c = -55;
Δ = b2-4ac
Δ = 112-4·11·(-55)
Δ = 2541
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:

$\sqrt{\Delta}=\sqrt{2541}=\sqrt{121*21}=\sqrt{121}*\sqrt{21}=11\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11\sqrt{21}}{2*11}=\frac{-11-11\sqrt{21}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11\sqrt{21}}{2*11}=\frac{-11+11\sqrt{21}}{22}
$