6x-10+65=x^2

Solution for 6x-10+65=x^2 equation:

6x-10+65=x^2

We move all terms to the left:

6x-10+65-(x^2)=0

determiningTheFunctionDomain
-x^2+6x-10+65=0

We add all the numbers together, and all the variables

-1x^2+6x+55=0

a = -1; b = 6; c = +55;
Δ = b2-4ac
Δ = 62-4·(-1)·55
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-16}{2*-1}=\frac{-22}{-2}
=+11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+16}{2*-1}=\frac{10}{-2}
=-5
$