p^2-10p-30=-23

Solution for p^2-10p-30=-23 equation:

p^2-10p-30=-23

We move all terms to the left:

p^2-10p-30-(-23)=0

We add all the numbers together, and all the variables

p^2-10p-7=0

a = 1; b = -10; c = -7;
Δ = b2-4ac
Δ = -102-4·1·(-7)
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-8\sqrt{2}}{2*1}=\frac{10-8\sqrt{2}}{2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+8\sqrt{2}}{2*1}=\frac{10+8\sqrt{2}}{2}
$