3/4p+3=-p+15

Solution for 3/4p+3=-p+15 equation:

3/4p+3=-p+15

We move all terms to the left:

3/4p+3-(-p+15)=0


Domain of the equation: 4p!=0

p!=0/4

p!=0

p∈R


We add all the numbers together, and all the variables

3/4p-(-1p+15)+3=0

We get rid of parentheses

3/4p+1p-15+3=0

We multiply all the terms by the denominator


1p*4p-15*4p+3*4p+3=0

Wy multiply elements

4p^2-60p+12p+3=0

We add all the numbers together, and all the variables

4p^2-48p+3=0

a = 4; b = -48; c = +3;
Δ = b2-4ac
Δ = -482-4·4·3
Δ = 2256
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:

$\sqrt{\Delta}=\sqrt{2256}=\sqrt{16*141}=\sqrt{16}*\sqrt{141}=4\sqrt{141}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{141}}{2*4}=\frac{48-4\sqrt{141}}{8}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{141}}{2*4}=\frac{48+4\sqrt{141}}{8}
$