60-1/2p=p-30

Solution for 60-1/2p=p-30 equation:

60-1/2p=p-30

We move all terms to the left:

60-1/2p-(p-30)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R


We get rid of parentheses

-1/2p-p+30+60=0

We multiply all the terms by the denominator


-p*2p+30*2p+60*2p-1=0

Wy multiply elements

-2p^2+60p+120p-1=0

We add all the numbers together, and all the variables

-2p^2+180p-1=0

a = -2; b = 180; c = -1;
Δ = b2-4ac
Δ = 1802-4·(-2)·(-1)
Δ = 32392
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:

$\sqrt{\Delta}=\sqrt{32392}=\sqrt{4*8098}=\sqrt{4}*\sqrt{8098}=2\sqrt{8098}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-2\sqrt{8098}}{2*-2}=\frac{-180-2\sqrt{8098}}{-4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+2\sqrt{8098}}{2*-2}=\frac{-180+2\sqrt{8098}}{-4}
$