x^2=9+x/2

Solution for x^2=9+x/2 equation:

x^2=9+x/2

We move all terms to the left:

x^2-(9+x/2)=0

We add all the numbers together, and all the variables

x^2-(x/2+9)=0

We get rid of parentheses

x^2-x/2-9=0

We multiply all the terms by the denominator


x^2*2-x-9*2=0

We add all the numbers together, and all the variables

x^2*2-1x-18=0

Wy multiply elements

2x^2-1x-18=0

a = 2; b = -1; c = -18;
Δ = b2-4ac
Δ = -12-4·2·(-18)
Δ = 145
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{-(-1)-\sqrt{145}}{2*2}=\frac{1-\sqrt{145}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{145}}{2*2}=\frac{1+\sqrt{145}}{4}
$