4s+6/9s=42

Solution for 4s+6/9s=42 equation:

4s+6/9s=42

We move all terms to the left:

4s+6/9s-(42)=0


Domain of the equation: 9s!=0

s!=0/9

s!=0

s∈R


We multiply all the terms by the denominator


4s*9s-42*9s+6=0

Wy multiply elements

36s^2-378s+6=0

a = 36; b = -378; c = +6;
Δ = b2-4ac
Δ = -3782-4·36·6
Δ = 142020
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:

$\sqrt{\Delta}=\sqrt{142020}=\sqrt{36*3945}=\sqrt{36}*\sqrt{3945}=6\sqrt{3945}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-378)-6\sqrt{3945}}{2*36}=\frac{378-6\sqrt{3945}}{72}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-378)+6\sqrt{3945}}{2*36}=\frac{378+6\sqrt{3945}}{72}
$