x(11x+21)=54

Solution for x(11x+21)=54 equation:

x(11x+21)=54

We move all terms to the left:

x(11x+21)-(54)=0

We multiply parentheses

11x^2+21x-54=0

a = 11; b = 21; c = -54;
Δ = b2-4ac
Δ = 212-4·11·(-54)
Δ = 2817
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:

$\sqrt{\Delta}=\sqrt{2817}=\sqrt{9*313}=\sqrt{9}*\sqrt{313}=3\sqrt{313}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{313}}{2*11}=\frac{-21-3\sqrt{313}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{313}}{2*11}=\frac{-21+3\sqrt{313}}{22}
$