9x=2x^2+9

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

9x=2x^2+9

We move all terms to the left:

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

We get rid of parentheses

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

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

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3}{2*-2}=\frac{-12}{-4}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3}{2*-2}=\frac{-6}{-4}
=1+1/2
$