3-x^2=4+9x

Solution for 3-x^2=4+9x equation:

3-x^2=4+9x

We move all terms to the left:

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

We add all the numbers together, and all the variables

-x^2-(9x+4)+3=0

We add all the numbers together, and all the variables

-1x^2-(9x+4)+3=0

We get rid of parentheses

-1x^2-9x-4+3=0

We add all the numbers together, and all the variables

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

a = -1; b = -9; c = -1;
Δ = b2-4ac
Δ = -92-4·(-1)·(-1)
Δ = 77
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{77}}{2*-1}=\frac{9-\sqrt{77}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{77}}{2*-1}=\frac{9+\sqrt{77}}{-2}
$