6p-5=5(p+4)p=

Solution for 6p-5=5(p+4)p= equation:

6p-5=5(p+4)p=

We move all terms to the left:

6p-5-(5(p+4)p)=0


We calculate terms in parentheses: -(5(p+4)p), so:

5(p+4)p

We multiply parentheses

5p^2+20p

Back to the equation:

-(5p^2+20p)


We get rid of parentheses

-5p^2+6p-20p-5=0

We add all the numbers together, and all the variables

-5p^2-14p-5=0

a = -5; b = -14; c = -5;
Δ = b2-4ac
Δ = -142-4·(-5)·(-5)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-4\sqrt{6}}{2*-5}=\frac{14-4\sqrt{6}}{-10}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+4\sqrt{6}}{2*-5}=\frac{14+4\sqrt{6}}{-10}
$