x^2/9=x+2/2

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

x^2/9=x+2/2

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

x^2/9-x-1=0

We multiply all the terms by the denominator


x^2-x*9-1*9=0

We add all the numbers together, and all the variables

x^2-x*9-9=0

Wy multiply elements

x^2-9x-9=0

a = 1; b = -9; c = -9;
Δ = b2-4ac
Δ = -92-4·1·(-9)
Δ = 117
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{117}=\sqrt{9*13}=\sqrt{9}*\sqrt{13}=3\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{13}}{2*1}=\frac{9-3\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{13}}{2*1}=\frac{9+3\sqrt{13}}{2}
$