s+2/3s+10=64

Solution for s+2/3s+10=64 equation:

s+2/3s+10=64

We move all terms to the left:

s+2/3s+10-(64)=0


Domain of the equation: 3s!=0

s!=0/3

s!=0

s∈R


We add all the numbers together, and all the variables

s+2/3s-54=0

We multiply all the terms by the denominator


s*3s-54*3s+2=0

Wy multiply elements

3s^2-162s+2=0

a = 3; b = -162; c = +2;
Δ = b2-4ac
Δ = -1622-4·3·2
Δ = 26220
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:

$\sqrt{\Delta}=\sqrt{26220}=\sqrt{4*6555}=\sqrt{4}*\sqrt{6555}=2\sqrt{6555}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-162)-2\sqrt{6555}}{2*3}=\frac{162-2\sqrt{6555}}{6}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-162)+2\sqrt{6555}}{2*3}=\frac{162+2\sqrt{6555}}{6}
$