12/3=p-5/p-12

Solution for 12/3=p-5/p-12 equation:

12/3=p-5/p-12

We move all terms to the left:

12/3-(p-5/p-12)=0


Domain of the equation: p-12)!=0

p∈R


We add all the numbers together, and all the variables

-(p-5/p-12)+4=0

We get rid of parentheses

-p+5/p+12+4=0

We multiply all the terms by the denominator


-p*p+12*p+4*p+5=0

We add all the numbers together, and all the variables

16p-p*p+5=0

Wy multiply elements

-1p^2+16p+5=0

a = -1; b = 16; c = +5;
Δ = b2-4ac
Δ = 162-4·(-1)·5
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{69}}{2*-1}=\frac{-16-2\sqrt{69}}{-2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{69}}{2*-1}=\frac{-16+2\sqrt{69}}{-2}
$