6s=11/2s+18

Solution for 6s=11/2s+18 equation:

6s=11/2s+18

We move all terms to the left:

6s-(11/2s+18)=0


Domain of the equation: 2s+18)!=0

s∈R


We get rid of parentheses

6s-11/2s-18=0

We multiply all the terms by the denominator


6s*2s-18*2s-11=0

Wy multiply elements

12s^2-36s-11=0

a = 12; b = -36; c = -11;
Δ = b2-4ac
Δ = -362-4·12·(-11)
Δ = 1824
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:

$\sqrt{\Delta}=\sqrt{1824}=\sqrt{16*114}=\sqrt{16}*\sqrt{114}=4\sqrt{114}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{114}}{2*12}=\frac{36-4\sqrt{114}}{24}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{114}}{2*12}=\frac{36+4\sqrt{114}}{24}
$