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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-648x^2)/450x^2+(-1050x)/450x^2+(-525x)/450x^2=0

We multiply all the terms by the denominator


(-648x^2)+(-1050x)+(-525x)=0

We get rid of parentheses

-648x^2-1050x-525x=0

We add all the numbers together, and all the variables

-648x^2-1575x=0

a = -648; b = -1575; c = 0;
Δ = b2-4ac
Δ = -15752-4·(-648)·0
Δ = 2480625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2480625}=1575$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1575)-1575}{2*-648}=\frac{0}{-1296}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1575)+1575}{2*-648}=\frac{3150}{-1296}
=-2+31/72
$