5p^2-6=229

Solution for 5p^2-6=229 equation:

5p^2-6=229

We move all terms to the left:

5p^2-6-(229)=0

We add all the numbers together, and all the variables

5p^2-235=0

a = 5; b = 0; c = -235;
Δ = b2-4ac
Δ = 02-4·5·(-235)
Δ = 4700
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:

$\sqrt{\Delta}=\sqrt{4700}=\sqrt{100*47}=\sqrt{100}*\sqrt{47}=10\sqrt{47}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{47}}{2*5}=\frac{0-10\sqrt{47}}{10}
=-\frac{10\sqrt{47}}{10}
=-\sqrt{47}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{47}}{2*5}=\frac{0+10\sqrt{47}}{10}
=\frac{10\sqrt{47}}{10}
=\sqrt{47}
$