5p(p+4)+3p=66

Solution for 5p(p+4)+3p=66 equation:

5p(p+4)+3p=66

We move all terms to the left:

5p(p+4)+3p-(66)=0

We add all the numbers together, and all the variables

3p+5p(p+4)-66=0

We multiply parentheses

5p^2+3p+20p-66=0

We add all the numbers together, and all the variables

5p^2+23p-66=0

a = 5; b = 23; c = -66;
Δ = b2-4ac
Δ = 232-4·5·(-66)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-43}{2*5}=\frac{-66}{10}
=-6+3/5
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+43}{2*5}=\frac{20}{10}
=2
$