11p-3=1/2p+7

Solution for 11p-3=1/2p+7 equation:

11p-3=1/2p+7

We move all terms to the left:

11p-3-(1/2p+7)=0


Domain of the equation: 2p+7)!=0

p∈R


We get rid of parentheses

11p-1/2p-7-3=0

We multiply all the terms by the denominator


11p*2p-7*2p-3*2p-1=0

Wy multiply elements

22p^2-14p-6p-1=0

We add all the numbers together, and all the variables

22p^2-20p-1=0

a = 22; b = -20; c = -1;
Δ = b2-4ac
Δ = -202-4·22·(-1)
Δ = 488
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:

$\sqrt{\Delta}=\sqrt{488}=\sqrt{4*122}=\sqrt{4}*\sqrt{122}=2\sqrt{122}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{122}}{2*22}=\frac{20-2\sqrt{122}}{44}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{122}}{2*22}=\frac{20+2\sqrt{122}}{44}
$