p=(9)/(7)p+28

Solution for p=(9)/(7)p+28 equation:

p=(9)/(7)p+28

We move all terms to the left:

p-((9)/(7)p+28)=0


Domain of the equation: 7p+28)!=0

p∈R


We get rid of parentheses

p-9/7p-28=0

We multiply all the terms by the denominator


p*7p-28*7p-9=0

Wy multiply elements

7p^2-196p-9=0

a = 7; b = -196; c = -9;
Δ = b2-4ac
Δ = -1962-4·7·(-9)
Δ = 38668
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:

$\sqrt{\Delta}=\sqrt{38668}=\sqrt{4*9667}=\sqrt{4}*\sqrt{9667}=2\sqrt{9667}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-196)-2\sqrt{9667}}{2*7}=\frac{196-2\sqrt{9667}}{14}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-196)+2\sqrt{9667}}{2*7}=\frac{196+2\sqrt{9667}}{14}
$