1/2x-5=7/6x+4

Solution for 1/2x-5=7/6x+4 equation:

1/2x-5=7/6x+4

We move all terms to the left:

1/2x-5-(7/6x+4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 6x+4)!=0

x∈R


We get rid of parentheses

1/2x-7/6x-4-5=0

We calculate fractions


6x/12x^2+(-14x)/12x^2-4-5=0

We add all the numbers together, and all the variables

6x/12x^2+(-14x)/12x^2-9=0

We multiply all the terms by the denominator


6x+(-14x)-9*12x^2=0

Wy multiply elements

-108x^2+6x+(-14x)=0

We get rid of parentheses

-108x^2+6x-14x=0

We add all the numbers together, and all the variables

-108x^2-8x=0

a = -108; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-108)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*-108}=\frac{0}{-216}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-108}=\frac{16}{-216}
=-2/27
$