p-18=1/2p-5

Solution for p-18=1/2p-5 equation:

p-18=1/2p-5

We move all terms to the left:

p-18-(1/2p-5)=0


Domain of the equation: 2p-5)!=0

p∈R


We get rid of parentheses

p-1/2p+5-18=0

We multiply all the terms by the denominator


p*2p+5*2p-18*2p-1=0

Wy multiply elements

2p^2+10p-36p-1=0

We add all the numbers together, and all the variables

2p^2-26p-1=0

a = 2; b = -26; c = -1;
Δ = b2-4ac
Δ = -262-4·2·(-1)
Δ = 684
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:

$\sqrt{\Delta}=\sqrt{684}=\sqrt{36*19}=\sqrt{36}*\sqrt{19}=6\sqrt{19}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-6\sqrt{19}}{2*2}=\frac{26-6\sqrt{19}}{4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+6\sqrt{19}}{2*2}=\frac{26+6\sqrt{19}}{4}
$