P(x)=(5x-1)(2x+2)

Solution for P(x)=(5x-1)(2x+2) equation:

(P)=(5P-1)(2P+2)

We move all terms to the left:

(P)-((5P-1)(2P+2))=0

We multiply parentheses ..

-((+10P^2+10P-2P-2))+P=0


We calculate terms in parentheses: -((+10P^2+10P-2P-2)), so:

(+10P^2+10P-2P-2)

We get rid of parentheses

10P^2+10P-2P-2

We add all the numbers together, and all the variables

10P^2+8P-2

Back to the equation:

-(10P^2+8P-2)


We add all the numbers together, and all the variables

P-(10P^2+8P-2)=0

We get rid of parentheses

-10P^2+P-8P+2=0

We add all the numbers together, and all the variables

-10P^2-7P+2=0

a = -10; b = -7; c = +2;
Δ = b2-4ac
Δ = -72-4·(-10)·2
Δ = 129
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{-(-7)-\sqrt{129}}{2*-10}=\frac{7-\sqrt{129}}{-20}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{129}}{2*-10}=\frac{7+\sqrt{129}}{-20}
$