(1/3)x+5/6=161/6

Solution for (1/3)x+5/6=161/6 equation:

(1/3)x+5/6=161/6

We move all terms to the left:

(1/3)x+5/6-(161/6)=0


Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/3)x+5/6-(+161/6)=0

We multiply parentheses

x^2+5/6-(+161/6)=0

We get rid of parentheses

x^2+5/6-161/6=0

We multiply all the terms by the denominator


x^2*6+5-161=0

We add all the numbers together, and all the variables

x^2*6-156=0

Wy multiply elements

6x^2-156=0

a = 6; b = 0; c = -156;
Δ = b2-4ac
Δ = 02-4·6·(-156)
Δ = 3744
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:

$\sqrt{\Delta}=\sqrt{3744}=\sqrt{144*26}=\sqrt{144}*\sqrt{26}=12\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{26}}{2*6}=\frac{0-12\sqrt{26}}{12}
=-\frac{12\sqrt{26}}{12}
=-\sqrt{26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{26}}{2*6}=\frac{0+12\sqrt{26}}{12}
=\frac{12\sqrt{26}}{12}
=\sqrt{26}
$