9x+6=x^2+4

Solution for 9x+6=x^2+4 equation:

9x+6=x^2+4

We move all terms to the left:

9x+6-(x^2+4)=0

We get rid of parentheses

-x^2+9x-4+6=0

We add all the numbers together, and all the variables

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

a = -1; b = 9; c = +2;
Δ = b2-4ac
Δ = 92-4·(-1)·2
Δ = 89
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{89}}{2*-1}=\frac{-9-\sqrt{89}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{89}}{2*-1}=\frac{-9+\sqrt{89}}{-2}
$