4p-3p(p+5)=3p-17

Solution for 4p-3p(p+5)=3p-17 equation:

4p-3p(p+5)=3p-17

We move all terms to the left:

4p-3p(p+5)-(3p-17)=0

We multiply parentheses

-3p^2+4p-15p-(3p-17)=0

We get rid of parentheses

-3p^2+4p-15p-3p+17=0

We add all the numbers together, and all the variables

-3p^2-14p+17=0

a = -3; b = -14; c = +17;
Δ = b2-4ac
Δ = -142-4·(-3)·17
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-20}{2*-3}=\frac{-6}{-6}
=1
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+20}{2*-3}=\frac{34}{-6}
=-5+2/3
$