(3/5)(p+3)=8

Solution for (3/5)(p+3)=8 equation:

(3/5)(p+3)=8

We move all terms to the left:

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


Domain of the equation: 5)(p+3)!=0

p∈R


We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+3p^2+3/5*3)-8=0

We multiply all the terms by the denominator


(+3p^2+3-8*5*3)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

3p^2-117=0

a = 3; b = 0; c = -117;
Δ = b2-4ac
Δ = 02-4·3·(-117)
Δ = 1404
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:

$\sqrt{\Delta}=\sqrt{1404}=\sqrt{36*39}=\sqrt{36}*\sqrt{39}=6\sqrt{39}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{39}}{2*3}=\frac{0-6\sqrt{39}}{6}
=-\frac{6\sqrt{39}}{6}
=-\sqrt{39}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{39}}{2*3}=\frac{0+6\sqrt{39}}{6}
=\frac{6\sqrt{39}}{6}
=\sqrt{39}
$