11/8p=2p+7

Solution for 11/8p=2p+7 equation:

11/8p=2p+7

We move all terms to the left:

11/8p-(2p+7)=0


Domain of the equation: 8p!=0

p!=0/8

p!=0

p∈R


We get rid of parentheses

11/8p-2p-7=0

We multiply all the terms by the denominator


-2p*8p-7*8p+11=0

Wy multiply elements

-16p^2-56p+11=0

a = -16; b = -56; c = +11;
Δ = b2-4ac
Δ = -562-4·(-16)·11
Δ = 3840
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:

$\sqrt{\Delta}=\sqrt{3840}=\sqrt{256*15}=\sqrt{256}*\sqrt{15}=16\sqrt{15}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-16\sqrt{15}}{2*-16}=\frac{56-16\sqrt{15}}{-32}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+16\sqrt{15}}{2*-16}=\frac{56+16\sqrt{15}}{-32}
$