5p^2-2=423

Solution for 5p^2-2=423 equation:

5p^2-2=423

We move all terms to the left:

5p^2-2-(423)=0

We add all the numbers together, and all the variables

5p^2-425=0

a = 5; b = 0; c = -425;
Δ = b2-4ac
Δ = 02-4·5·(-425)
Δ = 8500
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:

$\sqrt{\Delta}=\sqrt{8500}=\sqrt{100*85}=\sqrt{100}*\sqrt{85}=10\sqrt{85}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{85}}{2*5}=\frac{0-10\sqrt{85}}{10}
=-\frac{10\sqrt{85}}{10}
=-\sqrt{85}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{85}}{2*5}=\frac{0+10\sqrt{85}}{10}
=\frac{10\sqrt{85}}{10}
=\sqrt{85}
$