11x2-9x+1=11x

Solution for 11x2-9x+1=11x equation:

11x^2-9x+1=11x

We move all terms to the left:

11x^2-9x+1-(11x)=0

We add all the numbers together, and all the variables

11x^2-20x+1=0

a = 11; b = -20; c = +1;
Δ = b2-4ac
Δ = -202-4·11·1
Δ = 356
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:

$\sqrt{\Delta}=\sqrt{356}=\sqrt{4*89}=\sqrt{4}*\sqrt{89}=2\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{89}}{2*11}=\frac{20-2\sqrt{89}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{89}}{2*11}=\frac{20+2\sqrt{89}}{22}
$