7p^2+2=205

Solution for 7p^2+2=205 equation:

7p^2+2=205

We move all terms to the left:

7p^2+2-(205)=0

We add all the numbers together, and all the variables

7p^2-203=0

a = 7; b = 0; c = -203;
Δ = b2-4ac
Δ = 02-4·7·(-203)
Δ = 5684
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:

$\sqrt{\Delta}=\sqrt{5684}=\sqrt{196*29}=\sqrt{196}*\sqrt{29}=14\sqrt{29}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{29}}{2*7}=\frac{0-14\sqrt{29}}{14}
=-\frac{14\sqrt{29}}{14}
=-\sqrt{29}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{29}}{2*7}=\frac{0+14\sqrt{29}}{14}
=\frac{14\sqrt{29}}{14}
=\sqrt{29}
$