(5p+1)(p+1)=2(7p+5)

Solution for (5p+1)(p+1)=2(7p+5) equation:

(5p+1)(p+1)=2(7p+5)

We move all terms to the left:

(5p+1)(p+1)-(2(7p+5))=0

We multiply parentheses ..

(+5p^2+5p+p+1)-(2(7p+5))=0


We calculate terms in parentheses: -(2(7p+5)), so:

2(7p+5)

We multiply parentheses

14p+10

Back to the equation:

-(14p+10)


We get rid of parentheses

5p^2+5p+p-14p+1-10=0

We add all the numbers together, and all the variables

5p^2-8p-9=0

a = 5; b = -8; c = -9;
Δ = b2-4ac
Δ = -82-4·5·(-9)
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{61}}{2*5}=\frac{8-2\sqrt{61}}{10}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{61}}{2*5}=\frac{8+2\sqrt{61}}{10}
$