1/4p-3p=4

Solution for 1/4p-3p=4 equation:

1/4p-3p=4

We move all terms to the left:

1/4p-3p-(4)=0


Domain of the equation: 4p!=0

p!=0/4

p!=0

p∈R


We add all the numbers together, and all the variables

-3p+1/4p-4=0

We multiply all the terms by the denominator


-3p*4p-4*4p+1=0

Wy multiply elements

-12p^2-16p+1=0

a = -12; b = -16; c = +1;
Δ = b2-4ac
Δ = -162-4·(-12)·1
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{19}}{2*-12}=\frac{16-4\sqrt{19}}{-24}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{19}}{2*-12}=\frac{16+4\sqrt{19}}{-24}
$