-3/4p+3=1.25p-2

Solution for -3/4p+3=1.25p-2 equation:

-3/4p+3=1.25p-2

We move all terms to the left:

-3/4p+3-(1.25p-2)=0


Domain of the equation: 4p!=0

p!=0/4

p!=0

p∈R


We get rid of parentheses

-3/4p-1.25p+2+3=0

We multiply all the terms by the denominator


-(1.25p)*4p+2*4p+3*4p-3=0

We add all the numbers together, and all the variables

-(+1.25p)*4p+2*4p+3*4p-3=0

We multiply parentheses

-4p^2+2*4p+3*4p-3=0

Wy multiply elements

-4p^2+8p+12p-3=0

We add all the numbers together, and all the variables

-4p^2+20p-3=0

a = -4; b = 20; c = -3;
Δ = b2-4ac
Δ = 202-4·(-4)·(-3)
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{22}}{2*-4}=\frac{-20-4\sqrt{22}}{-8}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{22}}{2*-4}=\frac{-20+4\sqrt{22}}{-8}
$