6p-2(1+p)=1p+3p(1-p)

Solution for 6p-2(1+p)=1p+3p(1-p) equation:

6p-2(1+p)=1p+3p(1-p)

We move all terms to the left:

6p-2(1+p)-(1p+3p(1-p))=0

We add all the numbers together, and all the variables

6p-2(p+1)-(1p+3p(-1p+1))=0

We multiply parentheses

6p-2p-(1p+3p(-1p+1))-2=0


We calculate terms in parentheses: -(1p+3p(-1p+1)), so:

1p+3p(-1p+1)

We add all the numbers together, and all the variables

p+3p(-1p+1)

We multiply parentheses

-3p^2+p+3p

We add all the numbers together, and all the variables

-3p^2+4p

Back to the equation:

-(-3p^2+4p)


We add all the numbers together, and all the variables

-(-3p^2+4p)+4p-2=0

We get rid of parentheses

3p^2-4p+4p-2=0

We add all the numbers together, and all the variables

3p^2-2=0

a = 3; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·3·(-2)
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{6}}{2*3}=\frac{0-2\sqrt{6}}{6}
=-\frac{2\sqrt{6}}{6}
=-\frac{\sqrt{6}}{3}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{6}}{2*3}=\frac{0+2\sqrt{6}}{6}
=\frac{2\sqrt{6}}{6}
=\frac{\sqrt{6}}{3}
$