12p+7=3/4p+9

Solution for 12p+7=3/4p+9 equation:

12p+7=3/4p+9

We move all terms to the left:

12p+7-(3/4p+9)=0


Domain of the equation: 4p+9)!=0

p∈R


We get rid of parentheses

12p-3/4p-9+7=0

We multiply all the terms by the denominator


12p*4p-9*4p+7*4p-3=0

Wy multiply elements

48p^2-36p+28p-3=0

We add all the numbers together, and all the variables

48p^2-8p-3=0

a = 48; b = -8; c = -3;
Δ = b2-4ac
Δ = -82-4·48·(-3)
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{10}}{2*48}=\frac{8-8\sqrt{10}}{96}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{10}}{2*48}=\frac{8+8\sqrt{10}}{96}
$