7p^2+3=213

Solution for 7p^2+3=213 equation:

7p^2+3=213

We move all terms to the left:

7p^2+3-(213)=0

We add all the numbers together, and all the variables

7p^2-210=0

a = 7; b = 0; c = -210;
Δ = b2-4ac
Δ = 02-4·7·(-210)
Δ = 5880
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:

$\sqrt{\Delta}=\sqrt{5880}=\sqrt{196*30}=\sqrt{196}*\sqrt{30}=14\sqrt{30}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{30}}{2*7}=\frac{0-14\sqrt{30}}{14}
=-\frac{14\sqrt{30}}{14}
=-\sqrt{30}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{30}}{2*7}=\frac{0+14\sqrt{30}}{14}
=\frac{14\sqrt{30}}{14}
=\sqrt{30}
$