-7/3x-5/2=7/6x-7

Solution for -7/3x-5/2=7/6x-7 equation:

-7/3x-5/2=7/6x-7

We move all terms to the left:

-7/3x-5/2-(7/6x-7)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x-7)!=0

x∈R


We get rid of parentheses

-7/3x-7/6x+7-5/2=0

We calculate fractions


(-540x^2)/72x^2+(-168x)/72x^2+(-84x)/72x^2+7=0

We multiply all the terms by the denominator


(-540x^2)+(-168x)+(-84x)+7*72x^2=0

Wy multiply elements

(-540x^2)+504x^2+(-168x)+(-84x)=0

We get rid of parentheses

-540x^2+504x^2-168x-84x=0

We add all the numbers together, and all the variables

-36x^2-252x=0

a = -36; b = -252; c = 0;
Δ = b2-4ac
Δ = -2522-4·(-36)·0
Δ = 63504
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{63504}=252$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-252)-252}{2*-36}=\frac{0}{-72}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-252)+252}{2*-36}=\frac{504}{-72}
=-7
$