8p-(5/7)p+1=-5/4

Solution for 8p-(5/7)p+1=-5/4 equation:

8p-(5/7)p+1=-5/4

We move all terms to the left:

8p-(5/7)p+1-(-5/4)=0


Domain of the equation: 7)p!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

8p-(+5/7)p+1-(-5/4)=0

We multiply parentheses

-5p^2+8p+1-(-5/4)=0

We get rid of parentheses

-5p^2+8p+1+5/4=0

We multiply all the terms by the denominator


-5p^2*4+8p*4+5+1*4=0

We add all the numbers together, and all the variables

-5p^2*4+8p*4+9=0

Wy multiply elements

-20p^2+32p+9=0

a = -20; b = 32; c = +9;
Δ = b2-4ac
Δ = 322-4·(-20)·9
Δ = 1744
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:

$\sqrt{\Delta}=\sqrt{1744}=\sqrt{16*109}=\sqrt{16}*\sqrt{109}=4\sqrt{109}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{109}}{2*-20}=\frac{-32-4\sqrt{109}}{-40}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{109}}{2*-20}=\frac{-32+4\sqrt{109}}{-40}
$