-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


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


6x*2x+5*2x-6*2x-5=0

Wy multiply elements

12x^2+10x-12x-5=0

We add all the numbers together, and all the variables

12x^2-2x-5=0

a = 12; b = -2; c = -5;
Δ = b2-4ac
Δ = -22-4·12·(-5)
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{61}}{2*12}=\frac{2-2\sqrt{61}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{61}}{2*12}=\frac{2+2\sqrt{61}}{24}
$