3p-1=5(p-1)-2(7-2p)3p-1=5(p-1)-2(7-2p)

Solution for 3p-1=5(p-1)-2(7-2p)3p-1=5(p-1)-2(7-2p) equation:

3p-1=5(p-1)-2(7-2p)3p-1=5(p-1)-2(7-2p)

We move all terms to the left:

3p-1-(5(p-1)-2(7-2p)3p-1)=0

We add all the numbers together, and all the variables

3p-(5(p-1)-2(-2p+7)3p-1)-1=0


We calculate terms in parentheses: -(5(p-1)-2(-2p+7)3p-1), so:

5(p-1)-2(-2p+7)3p-1

We multiply parentheses

12p^2+5p-42p-5-1

We add all the numbers together, and all the variables

12p^2-37p-6

Back to the equation:

-(12p^2-37p-6)


We get rid of parentheses

-12p^2+3p+37p+6-1=0

We add all the numbers together, and all the variables

-12p^2+40p+5=0

a = -12; b = 40; c = +5;
Δ = b2-4ac
Δ = 402-4·(-12)·5
Δ = 1840
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:

$\sqrt{\Delta}=\sqrt{1840}=\sqrt{16*115}=\sqrt{16}*\sqrt{115}=4\sqrt{115}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{115}}{2*-12}=\frac{-40-4\sqrt{115}}{-24}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{115}}{2*-12}=\frac{-40+4\sqrt{115}}{-24}
$