p^2-40-7=0

Solution for p^2-40-7=0 equation:

p^2-40-7=0

We add all the numbers together, and all the variables

p^2-47=0

a = 1; b = 0; c = -47;
Δ = b2-4ac
Δ = 02-4·1·(-47)
Δ = 188
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:

$\sqrt{\Delta}=\sqrt{188}=\sqrt{4*47}=\sqrt{4}*\sqrt{47}=2\sqrt{47}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{47}}{2*1}=\frac{0-2\sqrt{47}}{2}
=-\frac{2\sqrt{47}}{2}
=-\sqrt{47}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{47}}{2*1}=\frac{0+2\sqrt{47}}{2}
=\frac{2\sqrt{47}}{2}
=\sqrt{47}
$