2.5(-3p-8)5p=4(2.25p+5.5)+15.5

Solution for 2.5(-3p-8)5p=4(2.25p+5.5)+15.5 equation:

2.5(-3p-8)5p=4(2.25p+5.5)+15.5

We move all terms to the left:

2.5(-3p-8)5p-(4(2.25p+5.5)+15.5)=0

We multiply parentheses

-36p^2-96p-(4(2.25p+5.5)+15.5)=0


We calculate terms in parentheses: -(4(2.25p+5.5)+15.5), so:

4(2.25p+5.5)+15.5

We multiply parentheses

8p+22+15.5

We add all the numbers together, and all the variables

8p+37.5

Back to the equation:

-(8p+37.5)


We get rid of parentheses

-36p^2-96p-8p-37.5=0

We add all the numbers together, and all the variables

-36p^2-104p-37.5=0

a = -36; b = -104; c = -37.5;
Δ = b2-4ac
Δ = -1042-4·(-36)·(-37.5)
Δ = 5416
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:

$\sqrt{\Delta}=\sqrt{5416}=\sqrt{4*1354}=\sqrt{4}*\sqrt{1354}=2\sqrt{1354}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-104)-2\sqrt{1354}}{2*-36}=\frac{104-2\sqrt{1354}}{-72}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-104)+2\sqrt{1354}}{2*-36}=\frac{104+2\sqrt{1354}}{-72}
$