(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∈R


We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+x^2+1/6*6)-11=0

We multiply all the terms by the denominator


(+x^2+1-11*6*6)=0

We get rid of parentheses

x^2+1-11*6*6=0

We add all the numbers together, and all the variables

x^2-395=0

a = 1; b = 0; c = -395;
Δ = b2-4ac
Δ = 02-4·1·(-395)
Δ = 1580
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:

$\sqrt{\Delta}=\sqrt{1580}=\sqrt{4*395}=\sqrt{4}*\sqrt{395}=2\sqrt{395}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{395}}{2*1}=\frac{0-2\sqrt{395}}{2}
=-\frac{2\sqrt{395}}{2}
=-\sqrt{395}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{395}}{2*1}=\frac{0+2\sqrt{395}}{2}
=\frac{2\sqrt{395}}{2}
=\sqrt{395}
$