-3/4p-3=1/8p-5

Solution for -3/4p-3=1/8p-5 equation:

-3/4p-3=1/8p-5

We move all terms to the left:

-3/4p-3-(1/8p-5)=0


Domain of the equation: 4p!=0

p!=0/4

p!=0

p∈R



Domain of the equation: 8p-5)!=0

p∈R


We get rid of parentheses

-3/4p-1/8p+5-3=0

We calculate fractions


(-24p)/32p^2+(-4p)/32p^2+5-3=0

We add all the numbers together, and all the variables

(-24p)/32p^2+(-4p)/32p^2+2=0

We multiply all the terms by the denominator


(-24p)+(-4p)+2*32p^2=0

Wy multiply elements

64p^2+(-24p)+(-4p)=0

We get rid of parentheses

64p^2-24p-4p=0

We add all the numbers together, and all the variables

64p^2-28p=0

a = 64; b = -28; c = 0;
Δ = b2-4ac
Δ = -282-4·64·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-28}{2*64}=\frac{0}{128}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+28}{2*64}=\frac{56}{128}
=7/16
$