-2p-3/2p=7

Solution for -2p-3/2p=7 equation:

-2p-3/2p=7

We move all terms to the left:

-2p-3/2p-(7)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R


We multiply all the terms by the denominator


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

Wy multiply elements

-4p^2-14p-3=0

a = -4; b = -14; c = -3;
Δ = b2-4ac
Δ = -142-4·(-4)·(-3)
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{37}}{2*-4}=\frac{14-2\sqrt{37}}{-8}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{37}}{2*-4}=\frac{14+2\sqrt{37}}{-8}
$