22-7=x^2-8x-16

Solution for 22-7=x^2-8x-16 equation:

22-7=x^2-8x-16

We move all terms to the left:

22-7-(x^2-8x-16)=0

We add all the numbers together, and all the variables

-(x^2-8x-16)+15=0

We get rid of parentheses

-x^2+8x+16+15=0

We add all the numbers together, and all the variables

-1x^2+8x+31=0

a = -1; b = 8; c = +31;
Δ = b2-4ac
Δ = 82-4·(-1)·31
Δ = 188
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:

$\sqrt{\Delta}=\sqrt{188}=\sqrt{4*47}=\sqrt{4}*\sqrt{47}=2\sqrt{47}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{47}}{2*-1}=\frac{-8-2\sqrt{47}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{47}}{2*-1}=\frac{-8+2\sqrt{47}}{-2}
$