11x^2-5x=x^2

Solution for 11x^2-5x=x^2 equation:

11x^2-5x=x^2

We move all terms to the left:

11x^2-5x-(x^2)=0

determiningTheFunctionDomain
11x^2-x^2-5x=0

We add all the numbers together, and all the variables

10x^2-5x=0

a = 10; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·10·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*10}=\frac{0}{20}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*10}=\frac{10}{20}
=1/2
$