(5p+3)(2p-3)=-2p(4p+13)-13

Solution for (5p+3)(2p-3)=-2p(4p+13)-13 equation:

(5p+3)(2p-3)=-2p(4p+13)-13

We move all terms to the left:

(5p+3)(2p-3)-(-2p(4p+13)-13)=0

We multiply parentheses ..

(+10p^2-15p+6p-9)-(-2p(4p+13)-13)=0


We calculate terms in parentheses: -(-2p(4p+13)-13), so:

-2p(4p+13)-13

We multiply parentheses

-8p^2-26p-13

Back to the equation:

-(-8p^2-26p-13)


We get rid of parentheses

10p^2+8p^2-15p+6p+26p-9+13=0

We add all the numbers together, and all the variables

18p^2+17p+4=0

a = 18; b = 17; c = +4;
Δ = b2-4ac
Δ = 172-4·18·4
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-1}{2*18}=\frac{-18}{36}
=-1/2
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+1}{2*18}=\frac{-16}{36}
=-4/9
$