5p-8/3p+9=7

Solution for 5p-8/3p+9=7 equation:

5p-8/3p+9=7

We move all terms to the left:

5p-8/3p+9-(7)=0


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R


We add all the numbers together, and all the variables

5p-8/3p+2=0

We multiply all the terms by the denominator


5p*3p+2*3p-8=0

Wy multiply elements

15p^2+6p-8=0

a = 15; b = 6; c = -8;
Δ = b2-4ac
Δ = 62-4·15·(-8)
Δ = 516
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:

$\sqrt{\Delta}=\sqrt{516}=\sqrt{4*129}=\sqrt{4}*\sqrt{129}=2\sqrt{129}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{129}}{2*15}=\frac{-6-2\sqrt{129}}{30}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{129}}{2*15}=\frac{-6+2\sqrt{129}}{30}
$