3(p+7)(4p-1)=5(2p-3)+1

Solution for 3(p+7)(4p-1)=5(2p-3)+1 equation:

3(p+7)(4p-1)=5(2p-3)+1

We move all terms to the left:

3(p+7)(4p-1)-(5(2p-3)+1)=0

We multiply parentheses ..

3(+4p^2-1p+28p-7)-(5(2p-3)+1)=0


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

5(2p-3)+1

We multiply parentheses

10p-15+1

We add all the numbers together, and all the variables

10p-14

Back to the equation:

-(10p-14)


We multiply parentheses

12p^2-3p+84p-(10p-14)-21=0

We get rid of parentheses

12p^2-3p+84p-10p+14-21=0

We add all the numbers together, and all the variables

12p^2+71p-7=0

a = 12; b = 71; c = -7;
Δ = b2-4ac
Δ = 712-4·12·(-7)
Δ = 5377
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(71)-\sqrt{5377}}{2*12}=\frac{-71-\sqrt{5377}}{24}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(71)+\sqrt{5377}}{2*12}=\frac{-71+\sqrt{5377}}{24}
$