7/2p-(p+4)=6

Solution for 7/2p-(p+4)=6 equation:

7/2p-(p+4)=6

We move all terms to the left:

7/2p-(p+4)-(6)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R


We get rid of parentheses

7/2p-p-4-6=0

We multiply all the terms by the denominator


-p*2p-4*2p-6*2p+7=0

Wy multiply elements

-2p^2-8p-12p+7=0

We add all the numbers together, and all the variables

-2p^2-20p+7=0

a = -2; b = -20; c = +7;
Δ = b2-4ac
Δ = -202-4·(-2)·7
Δ = 456
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:

$\sqrt{\Delta}=\sqrt{456}=\sqrt{4*114}=\sqrt{4}*\sqrt{114}=2\sqrt{114}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{114}}{2*-2}=\frac{20-2\sqrt{114}}{-4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{114}}{2*-2}=\frac{20+2\sqrt{114}}{-4}
$