5/6*x=42

Solution for 5/6*x=42 equation:

5/6*x=42

We move all terms to the left:

5/6*x-(42)=0


Domain of the equation: 6*x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-42*6*x+5=0

Wy multiply elements

-252x*x+5=0

Wy multiply elements

-252x^2+5=0

a = -252; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-252)·5
Δ = 5040
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5040}=\sqrt{144*35}=\sqrt{144}*\sqrt{35}=12\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{35}}{2*-252}=\frac{0-12\sqrt{35}}{-504}
=-\frac{12\sqrt{35}}{-504}
=-\frac{\sqrt{35}}{-42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{35}}{2*-252}=\frac{0+12\sqrt{35}}{-504}
=\frac{12\sqrt{35}}{-504}
=\frac{\sqrt{35}}{-42}
$