4-(1/6)x=17/6

Solution for 4-(1/6)x=17/6 equation:

4-(1/6)x=17/6

We move all terms to the left:

4-(1/6)x-(17/6)=0


Domain of the equation: 6)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+1/6)x+4-(+17/6)=0

We multiply parentheses

-x^2+4-(+17/6)=0

We get rid of parentheses

-x^2+4-17/6=0

We multiply all the terms by the denominator


-x^2*6-17+4*6=0

We add all the numbers together, and all the variables

-x^2*6+7=0

Wy multiply elements

-6x^2+7=0

a = -6; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-6)·7
Δ = 168
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:

$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{42}}{2*-6}=\frac{0-2\sqrt{42}}{-12}
=-\frac{2\sqrt{42}}{-12}
=-\frac{\sqrt{42}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{42}}{2*-6}=\frac{0+2\sqrt{42}}{-12}
=\frac{2\sqrt{42}}{-12}
=\frac{\sqrt{42}}{-6}
$