x(10x-2)=11

Solution for x(10x-2)=11 equation:

x(10x-2)=11

We move all terms to the left:

x(10x-2)-(11)=0

We multiply parentheses

10x^2-2x-11=0

a = 10; b = -2; c = -11;
Δ = b2-4ac
Δ = -22-4·10·(-11)
Δ = 444
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:

$\sqrt{\Delta}=\sqrt{444}=\sqrt{4*111}=\sqrt{4}*\sqrt{111}=2\sqrt{111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{111}}{2*10}=\frac{2-2\sqrt{111}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{111}}{2*10}=\frac{2+2\sqrt{111}}{20}
$