10-3p=2/3p+5

Solution for 10-3p=2/3p+5 equation:

10-3p=2/3p+5

We move all terms to the left:

10-3p-(2/3p+5)=0


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

p∈R


We get rid of parentheses

-3p-2/3p-5+10=0

We multiply all the terms by the denominator


-3p*3p-5*3p+10*3p-2=0

Wy multiply elements

-9p^2-15p+30p-2=0

We add all the numbers together, and all the variables

-9p^2+15p-2=0

a = -9; b = 15; c = -2;
Δ = b2-4ac
Δ = 152-4·(-9)·(-2)
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{17}}{2*-9}=\frac{-15-3\sqrt{17}}{-18}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{17}}{2*-9}=\frac{-15+3\sqrt{17}}{-18}
$