31/4p+4(3/4p-12)=79.25

Solution for 31/4p+4(3/4p-12)=79.25 equation:

31/4p+4(3/4p-12)=79.25

We move all terms to the left:

31/4p+4(3/4p-12)-(79.25)=0


Domain of the equation: 4p!=0

p!=0/4

p!=0

p∈R



Domain of the equation: 4p-12)!=0

p∈R


We add all the numbers together, and all the variables

31/4p+4(3/4p-12)-79.25=0

We multiply parentheses

31/4p+12p-48-79.25=0

We multiply all the terms by the denominator


12p*4p-48*4p-(79.25)*4p+31=0

We multiply parentheses

12p*4p-48*4p-317p+31=0

Wy multiply elements

48p^2-192p-317p+31=0

We add all the numbers together, and all the variables

48p^2-509p+31=0

a = 48; b = -509; c = +31;
Δ = b2-4ac
Δ = -5092-4·48·31
Δ = 253129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-509)-\sqrt{253129}}{2*48}=\frac{509-\sqrt{253129}}{96}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-509)+\sqrt{253129}}{2*48}=\frac{509+\sqrt{253129}}{96}
$