23/46p-2p=-6

Solution for 23/46p-2p=-6 equation:

23/46p-2p=-6

We move all terms to the left:

23/46p-2p-(-6)=0


Domain of the equation: 46p!=0

p!=0/46

p!=0

p∈R


We add all the numbers together, and all the variables

-2p+23/46p+6=0

We multiply all the terms by the denominator


-2p*46p+6*46p+23=0

Wy multiply elements

-92p^2+276p+23=0

a = -92; b = 276; c = +23;
Δ = b2-4ac
Δ = 2762-4·(-92)·23
Δ = 84640
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:

$\sqrt{\Delta}=\sqrt{84640}=\sqrt{8464*10}=\sqrt{8464}*\sqrt{10}=92\sqrt{10}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(276)-92\sqrt{10}}{2*-92}=\frac{-276-92\sqrt{10}}{-184}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(276)+92\sqrt{10}}{2*-92}=\frac{-276+92\sqrt{10}}{-184}
$