11x(x+2)=77

Solution for 11x(x+2)=77 equation:

11x(x+2)=77

We move all terms to the left:

11x(x+2)-(77)=0

We multiply parentheses

11x^2+22x-77=0

a = 11; b = 22; c = -77;
Δ = b2-4ac
Δ = 222-4·11·(-77)
Δ = 3872
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:

$\sqrt{\Delta}=\sqrt{3872}=\sqrt{1936*2}=\sqrt{1936}*\sqrt{2}=44\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-44\sqrt{2}}{2*11}=\frac{-22-44\sqrt{2}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+44\sqrt{2}}{2*11}=\frac{-22+44\sqrt{2}}{22}
$