4x+9=x2-15

Solution for 4x+9=x2-15 equation:

4x+9=x2-15

We move all terms to the left:

4x+9-(x2-15)=0

We add all the numbers together, and all the variables

-(+x^2-15)+4x+9=0

We get rid of parentheses

-x^2+4x+15+9=0

We add all the numbers together, and all the variables

-1x^2+4x+24=0

a = -1; b = 4; c = +24;
Δ = b2-4ac
Δ = 42-4·(-1)·24
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{7}}{2*-1}=\frac{-4-4\sqrt{7}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{7}}{2*-1}=\frac{-4+4\sqrt{7}}{-2}
$