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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

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

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

We get rid of parentheses

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

We calculate fractions


(-30x)/12x^2+8x/12x^2+1-6=0

We add all the numbers together, and all the variables

(-30x)/12x^2+8x/12x^2-5=0

We multiply all the terms by the denominator


(-30x)+8x-5*12x^2=0

We add all the numbers together, and all the variables

8x+(-30x)-5*12x^2=0

Wy multiply elements

-60x^2+8x+(-30x)=0

We get rid of parentheses

-60x^2+8x-30x=0

We add all the numbers together, and all the variables

-60x^2-22x=0

a = -60; b = -22; c = 0;
Δ = b2-4ac
Δ = -222-4·(-60)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-22}{2*-60}=\frac{0}{-120}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+22}{2*-60}=\frac{44}{-120}
=-11/30
$