183=8s+3/2s+12

Solution for 183=8s+3/2s+12 equation:

183=8s+3/2s+12

We move all terms to the left:

183-(8s+3/2s+12)=0


Domain of the equation: 2s+12)!=0

s∈R


We get rid of parentheses

-8s-3/2s-12+183=0

We multiply all the terms by the denominator


-8s*2s-12*2s+183*2s-3=0

Wy multiply elements

-16s^2-24s+366s-3=0

We add all the numbers together, and all the variables

-16s^2+342s-3=0

a = -16; b = 342; c = -3;
Δ = b2-4ac
Δ = 3422-4·(-16)·(-3)
Δ = 116772
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:

$\sqrt{\Delta}=\sqrt{116772}=\sqrt{4*29193}=\sqrt{4}*\sqrt{29193}=2\sqrt{29193}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(342)-2\sqrt{29193}}{2*-16}=\frac{-342-2\sqrt{29193}}{-32}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(342)+2\sqrt{29193}}{2*-16}=\frac{-342+2\sqrt{29193}}{-32}
$