(5/8)s-(7/8)=s+1

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

(5/8)s-(7/8)=s+1

We move all terms to the left:

(5/8)s-(7/8)-(s+1)=0


Domain of the equation: 8)s!=0

s!=0/1

s!=0

s∈R


We add all the numbers together, and all the variables

(+5/8)s-(s+1)-(+7/8)=0

We multiply parentheses

5s^2-(s+1)-(+7/8)=0

We get rid of parentheses

5s^2-s-1-7/8=0

We multiply all the terms by the denominator


5s^2*8-s*8-7-1*8=0

We add all the numbers together, and all the variables

5s^2*8-s*8-15=0

Wy multiply elements

40s^2-8s-15=0

a = 40; b = -8; c = -15;
Δ = b2-4ac
Δ = -82-4·40·(-15)
Δ = 2464
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2464}=\sqrt{16*154}=\sqrt{16}*\sqrt{154}=4\sqrt{154}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{154}}{2*40}=\frac{8-4\sqrt{154}}{80}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{154}}{2*40}=\frac{8+4\sqrt{154}}{80}
$