7/2p-2=2p-17

Solution for 7/2p-2=2p-17 equation:

7/2p-2=2p-17

We move all terms to the left:

7/2p-2-(2p-17)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R


We get rid of parentheses

7/2p-2p+17-2=0

We multiply all the terms by the denominator


-2p*2p+17*2p-2*2p+7=0

Wy multiply elements

-4p^2+34p-4p+7=0

We add all the numbers together, and all the variables

-4p^2+30p+7=0

a = -4; b = 30; c = +7;
Δ = b2-4ac
Δ = 302-4·(-4)·7
Δ = 1012
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:

$\sqrt{\Delta}=\sqrt{1012}=\sqrt{4*253}=\sqrt{4}*\sqrt{253}=2\sqrt{253}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{253}}{2*-4}=\frac{-30-2\sqrt{253}}{-8}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{253}}{2*-4}=\frac{-30+2\sqrt{253}}{-8}
$