x^2-16=5x+2

Solution for x^2-16=5x+2 equation:

x^2-16=5x+2

We move all terms to the left:

x^2-16-(5x+2)=0

We get rid of parentheses

x^2-5x-2-16=0

We add all the numbers together, and all the variables

x^2-5x-18=0

a = 1; b = -5; c = -18;
Δ = b2-4ac
Δ = -52-4·1·(-18)
Δ = 97
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{-(-5)-\sqrt{97}}{2*1}=\frac{5-\sqrt{97}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{97}}{2*1}=\frac{5+\sqrt{97}}{2}
$