s+9/2s+10=87

Solution for s+9/2s+10=87 equation:

s+9/2s+10=87

We move all terms to the left:

s+9/2s+10-(87)=0


Domain of the equation: 2s!=0

s!=0/2

s!=0

s∈R


We add all the numbers together, and all the variables

s+9/2s-77=0

We multiply all the terms by the denominator


s*2s-77*2s+9=0

Wy multiply elements

2s^2-154s+9=0

a = 2; b = -154; c = +9;
Δ = b2-4ac
Δ = -1542-4·2·9
Δ = 23644
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:

$\sqrt{\Delta}=\sqrt{23644}=\sqrt{4*5911}=\sqrt{4}*\sqrt{5911}=2\sqrt{5911}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-154)-2\sqrt{5911}}{2*2}=\frac{154-2\sqrt{5911}}{4}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-154)+2\sqrt{5911}}{2*2}=\frac{154+2\sqrt{5911}}{4}
$