(-5/6)x-(1/3)=-7

Solution for (-5/6)x-(1/3)=-7 equation:

(-5/6)x-(1/3)=-7

We move all terms to the left:

(-5/6)x-(1/3)-(-7)=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

(-5/6)x-(+1/3)-(-7)=0

We add all the numbers together, and all the variables

(-5/6)x+7-(+1/3)=0

We multiply parentheses

-5x^2+7-(+1/3)=0

We get rid of parentheses

-5x^2+7-1/3=0

We multiply all the terms by the denominator


-5x^2*3-1+7*3=0

We add all the numbers together, and all the variables

-5x^2*3+20=0

Wy multiply elements

-15x^2+20=0

a = -15; b = 0; c = +20;
Δ = b2-4ac
Δ = 02-4·(-15)·20
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{3}}{2*-15}=\frac{0-20\sqrt{3}}{-30}
=-\frac{20\sqrt{3}}{-30}
=-\frac{2\sqrt{3}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{3}}{2*-15}=\frac{0+20\sqrt{3}}{-30}
=\frac{20\sqrt{3}}{-30}
=\frac{2\sqrt{3}}{-3}
$