p-3/4p=28

Solution for p-3/4p=28 equation:

p-3/4p=28

We move all terms to the left:

p-3/4p-(28)=0


Domain of the equation: 4p!=0

p!=0/4

p!=0

p∈R


We multiply all the terms by the denominator


p*4p-28*4p-3=0

Wy multiply elements

4p^2-112p-3=0

a = 4; b = -112; c = -3;
Δ = b2-4ac
Δ = -1122-4·4·(-3)
Δ = 12592
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:

$\sqrt{\Delta}=\sqrt{12592}=\sqrt{16*787}=\sqrt{16}*\sqrt{787}=4\sqrt{787}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-112)-4\sqrt{787}}{2*4}=\frac{112-4\sqrt{787}}{8}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-112)+4\sqrt{787}}{2*4}=\frac{112+4\sqrt{787}}{8}
$