p^2-4p-68=6

Solution for p^2-4p-68=6 equation:

p^2-4p-68=6

We move all terms to the left:

p^2-4p-68-(6)=0

We add all the numbers together, and all the variables

p^2-4p-74=0

a = 1; b = -4; c = -74;
Δ = b2-4ac
Δ = -42-4·1·(-74)
Δ = 312
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{312}=\sqrt{4*78}=\sqrt{4}*\sqrt{78}=2\sqrt{78}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{78}}{2*1}=\frac{4-2\sqrt{78}}{2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{78}}{2*1}=\frac{4+2\sqrt{78}}{2}
$