2(9x-38.5)=x^2

Solution for 2(9x-38.5)=x^2 equation:

2(9x-38.5)=x^2

We move all terms to the left:

2(9x-38.5)-(x^2)=0

determiningTheFunctionDomain
-x^2+2(9x-38.5)=0

We add all the numbers together, and all the variables

-1x^2+2(9x-38.5)=0

We multiply parentheses

-1x^2+18x-77=0

a = -1; b = 18; c = -77;
Δ = b2-4ac
Δ = 182-4·(-1)·(-77)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-4}{2*-1}=\frac{-22}{-2}
=+11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+4}{2*-1}=\frac{-14}{-2}
=+7
$