-3p(8p-11)=-5p-5

Solution for -3p(8p-11)=-5p-5 equation:

-3p(8p-11)=-5p-5

We move all terms to the left:

-3p(8p-11)-(-5p-5)=0

We multiply parentheses

-24p^2+33p-(-5p-5)=0

We get rid of parentheses

-24p^2+33p+5p+5=0

We add all the numbers together, and all the variables

-24p^2+38p+5=0

a = -24; b = 38; c = +5;
Δ = b2-4ac
Δ = 382-4·(-24)·5
Δ = 1924
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:

$\sqrt{\Delta}=\sqrt{1924}=\sqrt{4*481}=\sqrt{4}*\sqrt{481}=2\sqrt{481}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-2\sqrt{481}}{2*-24}=\frac{-38-2\sqrt{481}}{-48}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+2\sqrt{481}}{2*-24}=\frac{-38+2\sqrt{481}}{-48}
$