2p-3=3/4p+7

Solution for 2p-3=3/4p+7 equation:

2p-3=3/4p+7

We move all terms to the left:

2p-3-(3/4p+7)=0


Domain of the equation: 4p+7)!=0

p∈R


We get rid of parentheses

2p-3/4p-7-3=0

We multiply all the terms by the denominator


2p*4p-7*4p-3*4p-3=0

Wy multiply elements

8p^2-28p-12p-3=0

We add all the numbers together, and all the variables

8p^2-40p-3=0

a = 8; b = -40; c = -3;
Δ = b2-4ac
Δ = -402-4·8·(-3)
Δ = 1696
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:

$\sqrt{\Delta}=\sqrt{1696}=\sqrt{16*106}=\sqrt{16}*\sqrt{106}=4\sqrt{106}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{106}}{2*8}=\frac{40-4\sqrt{106}}{16}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{106}}{2*8}=\frac{40+4\sqrt{106}}{16}
$