-4p(-6p+20)-18=-5(15p-20)

Solution for -4p(-6p+20)-18=-5(15p-20) equation:

-4p(-6p+20)-18=-5(15p-20)

We move all terms to the left:

-4p(-6p+20)-18-(-5(15p-20))=0

We multiply parentheses

24p^2-80p-(-5(15p-20))-18=0


We calculate terms in parentheses: -(-5(15p-20)), so:

-5(15p-20)

We multiply parentheses

-75p+100

Back to the equation:

-(-75p+100)


We get rid of parentheses

24p^2-80p+75p-100-18=0

We add all the numbers together, and all the variables

24p^2-5p-118=0

a = 24; b = -5; c = -118;
Δ = b2-4ac
Δ = -52-4·24·(-118)
Δ = 11353
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{-(-5)-\sqrt{11353}}{2*24}=\frac{5-\sqrt{11353}}{48}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{11353}}{2*24}=\frac{5+\sqrt{11353}}{48}
$