x=0.5x^2-8x+37

Solution for x=0.5x^2-8x+37 equation:

x=0.5x^2-8x+37

We move all terms to the left:

x-(0.5x^2-8x+37)=0

We get rid of parentheses

-0.5x^2+x+8x-37=0

We add all the numbers together, and all the variables

-0.5x^2+9x-37=0

a = -0.5; b = 9; c = -37;
Δ = b2-4ac
Δ = 92-4·(-0.5)·(-37)
Δ = 7
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{-(9)-\sqrt{7}}{2*-0.5}=\frac{-9-\sqrt{7}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{7}}{2*-0.5}=\frac{-9+\sqrt{7}}{-1}
$