3/4*p=60

Solution for 3/4*p=60 equation:

3/4*p=60

We move all terms to the left:

3/4*p-(60)=0


Domain of the equation: 4*p!=0

p!=0/1

p!=0

p∈R


We multiply all the terms by the denominator


-60*4*p+3=0

Wy multiply elements

-240p*p+3=0

Wy multiply elements

-240p^2+3=0

a = -240; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-240)·3
Δ = 2880
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:

$\sqrt{\Delta}=\sqrt{2880}=\sqrt{576*5}=\sqrt{576}*\sqrt{5}=24\sqrt{5}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{5}}{2*-240}=\frac{0-24\sqrt{5}}{-480}
=-\frac{24\sqrt{5}}{-480}
=-\frac{\sqrt{5}}{-20}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{5}}{2*-240}=\frac{0+24\sqrt{5}}{-480}
=\frac{24\sqrt{5}}{-480}
=\frac{\sqrt{5}}{-20}
$