4/7p^2=20

Solution for 4/7p^2=20 equation:

4/7p^2=20

We move all terms to the left:

4/7p^2-(20)=0


Domain of the equation: 7p^2!=0

p^2!=0/7

p^2!=√0

p!=0

p∈R


We multiply all the terms by the denominator


-20*7p^2+4=0

Wy multiply elements

-140p^2+4=0

a = -140; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-140)·4
Δ = 2240
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:

$\sqrt{\Delta}=\sqrt{2240}=\sqrt{64*35}=\sqrt{64}*\sqrt{35}=8\sqrt{35}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{35}}{2*-140}=\frac{0-8\sqrt{35}}{-280}
=-\frac{8\sqrt{35}}{-280}
=-\frac{\sqrt{35}}{-35}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{35}}{2*-140}=\frac{0+8\sqrt{35}}{-280}
=\frac{8\sqrt{35}}{-280}
=\frac{\sqrt{35}}{-35}
$