8-1/2s=15+2s

Solution for 8-1/2s=15+2s equation:

8-1/2s=15+2s

We move all terms to the left:

8-1/2s-(15+2s)=0


Domain of the equation: 2s!=0

s!=0/2

s!=0

s∈R


We add all the numbers together, and all the variables

-1/2s-(2s+15)+8=0

We get rid of parentheses

-1/2s-2s-15+8=0

We multiply all the terms by the denominator


-2s*2s-15*2s+8*2s-1=0

Wy multiply elements

-4s^2-30s+16s-1=0

We add all the numbers together, and all the variables

-4s^2-14s-1=0

a = -4; b = -14; c = -1;
Δ = b2-4ac
Δ = -142-4·(-4)·(-1)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-6\sqrt{5}}{2*-4}=\frac{14-6\sqrt{5}}{-8}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+6\sqrt{5}}{2*-4}=\frac{14+6\sqrt{5}}{-8}
$