(1/3)(x+1)=11

Solution for (1/3)(x+1)=11 equation:

(1/3)(x+1)=11

We move all terms to the left:

(1/3)(x+1)-(11)=0


Domain of the equation: 3)(x+1)!=0

x∈R


We add all the numbers together, and all the variables

(+1/3)(x+1)-11=0

We multiply parentheses ..

(+x^2+1/3*1)-11=0

We multiply all the terms by the denominator


(+x^2+1-11*3*1)=0

We get rid of parentheses

x^2+1-11*3*1=0

We add all the numbers together, and all the variables

x^2-32=0

a = 1; b = 0; c = -32;
Δ = b2-4ac
Δ = 02-4·1·(-32)
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{2}}{2*1}=\frac{0-8\sqrt{2}}{2}
=-\frac{8\sqrt{2}}{2}
=-4\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{2}}{2*1}=\frac{0+8\sqrt{2}}{2}
=\frac{8\sqrt{2}}{2}
=4\sqrt{2}
$