(11x-3)(11x-3)=30

Solution for (11x-3)(11x-3)=30 equation:

(11x-3)(11x-3)=30

We move all terms to the left:

(11x-3)(11x-3)-(30)=0

We multiply parentheses ..

(+121x^2-33x-33x+9)-30=0

We get rid of parentheses

121x^2-33x-33x+9-30=0

We add all the numbers together, and all the variables

121x^2-66x-21=0

a = 121; b = -66; c = -21;
Δ = b2-4ac
Δ = -662-4·121·(-21)
Δ = 14520
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:

$\sqrt{\Delta}=\sqrt{14520}=\sqrt{484*30}=\sqrt{484}*\sqrt{30}=22\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-22\sqrt{30}}{2*121}=\frac{66-22\sqrt{30}}{242}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+22\sqrt{30}}{2*121}=\frac{66+22\sqrt{30}}{242}
$