9x^2-6=2x+9

Solution for 9x^2-6=2x+9 equation:

9x^2-6=2x+9

We move all terms to the left:

9x^2-6-(2x+9)=0

We get rid of parentheses

9x^2-2x-9-6=0

We add all the numbers together, and all the variables

9x^2-2x-15=0

a = 9; b = -2; c = -15;
Δ = b2-4ac
Δ = -22-4·9·(-15)
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{34}}{2*9}=\frac{2-4\sqrt{34}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{34}}{2*9}=\frac{2+4\sqrt{34}}{18}
$