11x-29=x^2

Solution for 11x-29=x^2 equation:

11x-29=x^2

We move all terms to the left:

11x-29-(x^2)=0

determiningTheFunctionDomain
-x^2+11x-29=0

We add all the numbers together, and all the variables

-1x^2+11x-29=0

a = -1; b = 11; c = -29;
Δ = b2-4ac
Δ = 112-4·(-1)·(-29)
Δ = 5
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{-(11)-\sqrt{5}}{2*-1}=\frac{-11-\sqrt{5}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{5}}{2*-1}=\frac{-11+\sqrt{5}}{-2}
$