(x-2)(x-2)=11x-4

Solution for (x-2)(x-2)=11x-4 equation:

(x-2)(x-2)=11x-4

We move all terms to the left:

(x-2)(x-2)-(11x-4)=0

We get rid of parentheses

(x-2)(x-2)-11x+4=0

We multiply parentheses ..

(+x^2-2x-2x+4)-11x+4=0

We get rid of parentheses

x^2-2x-2x-11x+4+4=0

We add all the numbers together, and all the variables

x^2-15x+8=0

a = 1; b = -15; c = +8;
Δ = b2-4ac
Δ = -152-4·1·8
Δ = 193
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{193}}{2*1}=\frac{15-\sqrt{193}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{193}}{2*1}=\frac{15+\sqrt{193}}{2}
$