1/6*x*6=11

Solution for 1/6*x*6=11 equation:

1/6*x*6=11

We move all terms to the left:

1/6*x*6-(11)=0


Domain of the equation: 6*x*6!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-11*6*x*6+1=0

Wy multiply elements

-396x*x+1=0

Wy multiply elements

-396x^2+1=0

a = -396; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-396)·1
Δ = 1584
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:

$\sqrt{\Delta}=\sqrt{1584}=\sqrt{144*11}=\sqrt{144}*\sqrt{11}=12\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{11}}{2*-396}=\frac{0-12\sqrt{11}}{-792}
=-\frac{12\sqrt{11}}{-792}
=-\frac{\sqrt{11}}{-66}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{11}}{2*-396}=\frac{0+12\sqrt{11}}{-792}
=\frac{12\sqrt{11}}{-792}
=\frac{\sqrt{11}}{-66}
$