(1/3)(24p-66)=3p+43

Solution for (1/3)(24p-66)=3p+43 equation:

(1/3)(24p-66)=3p+43

We move all terms to the left:

(1/3)(24p-66)-(3p+43)=0


Domain of the equation: 3)(24p-66)!=0

p∈R


We add all the numbers together, and all the variables

(+1/3)(24p-66)-(3p+43)=0

We get rid of parentheses

(+1/3)(24p-66)-3p-43=0

We multiply parentheses ..

(+24p^2+1/3*-66)-3p-43=0

We multiply all the terms by the denominator


(+24p^2+1-3p*3*-66)-43*3*-66)=0

We add all the numbers together, and all the variables

(+24p^2+1-3p*3*-66)=0

We get rid of parentheses

24p^2-3p*3*+1-66=0

We add all the numbers together, and all the variables

24p^2-3p*3*-65=0

Wy multiply elements

24p^2-9p^2-65=0

We add all the numbers together, and all the variables

15p^2-65=0

a = 15; b = 0; c = -65;
Δ = b2-4ac
Δ = 02-4·15·(-65)
Δ = 3900
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:

$\sqrt{\Delta}=\sqrt{3900}=\sqrt{100*39}=\sqrt{100}*\sqrt{39}=10\sqrt{39}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{39}}{2*15}=\frac{0-10\sqrt{39}}{30}
=-\frac{10\sqrt{39}}{30}
=-\frac{\sqrt{39}}{3}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{39}}{2*15}=\frac{0+10\sqrt{39}}{30}
=\frac{10\sqrt{39}}{30}
=\frac{\sqrt{39}}{3}
$