9x2=x+9

Solution for 9x2=x+9 equation:

9x^2=x+9

We move all terms to the left:

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

We get rid of parentheses

9x^2-x-9=0

We add all the numbers together, and all the variables

9x^2-1x-9=0

a = 9; b = -1; c = -9;
Δ = b2-4ac
Δ = -12-4·9·(-9)
Δ = 325
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:

$\sqrt{\Delta}=\sqrt{325}=\sqrt{25*13}=\sqrt{25}*\sqrt{13}=5\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-5\sqrt{13}}{2*9}=\frac{1-5\sqrt{13}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+5\sqrt{13}}{2*9}=\frac{1+5\sqrt{13}}{18}
$