9-x=2x^2+5x+6

Solution for 9-x=2x^2+5x+6 equation:

9-x=2x^2+5x+6

We move all terms to the left:

9-x-(2x^2+5x+6)=0

We add all the numbers together, and all the variables

-1x-(2x^2+5x+6)+9=0

We get rid of parentheses

-2x^2-1x-5x-6+9=0

We add all the numbers together, and all the variables

-2x^2-6x+3=0

a = -2; b = -6; c = +3;
Δ = b2-4ac
Δ = -62-4·(-2)·3
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{15}}{2*-2}=\frac{6-2\sqrt{15}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{15}}{2*-2}=\frac{6+2\sqrt{15}}{-4}
$