(x-11)x=53

Solution for (x-11)x=53 equation:

(x-11)x=53

We move all terms to the left:

(x-11)x-(53)=0

We multiply parentheses

x^2-11x-53=0

a = 1; b = -11; c = -53;
Δ = b2-4ac
Δ = -112-4·1·(-53)
Δ = 333
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:

$\sqrt{\Delta}=\sqrt{333}=\sqrt{9*37}=\sqrt{9}*\sqrt{37}=3\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-3\sqrt{37}}{2*1}=\frac{11-3\sqrt{37}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+3\sqrt{37}}{2*1}=\frac{11+3\sqrt{37}}{2}
$