3/4s=6s+18

Solution for 3/4s=6s+18 equation:

3/4s=6s+18

We move all terms to the left:

3/4s-(6s+18)=0


Domain of the equation: 4s!=0

s!=0/4

s!=0

s∈R


We get rid of parentheses

3/4s-6s-18=0

We multiply all the terms by the denominator


-6s*4s-18*4s+3=0

Wy multiply elements

-24s^2-72s+3=0

a = -24; b = -72; c = +3;
Δ = b2-4ac
Δ = -722-4·(-24)·3
Δ = 5472
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:

$\sqrt{\Delta}=\sqrt{5472}=\sqrt{144*38}=\sqrt{144}*\sqrt{38}=12\sqrt{38}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-12\sqrt{38}}{2*-24}=\frac{72-12\sqrt{38}}{-48}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+12\sqrt{38}}{2*-24}=\frac{72+12\sqrt{38}}{-48}
$