6x-5-2x+8=12(1/3x+0.25)

Solution for 6x-5-2x+8=12(1/3x+0.25) equation:

6x-5-2x+8=12(1/3x+0.25)

We move all terms to the left:

6x-5-2x+8-(12(1/3x+0.25))=0


Domain of the equation: 3x+0.25))!=0

x∈R


We add all the numbers together, and all the variables

4x-(12(1/3x+0.25))+3=0

We multiply all the terms by the denominator


4x*3x+3*3x+0.25))-(12(1+0.25))=0

We add all the numbers together, and all the variables

4x*3x+3*3x+0.25))-(12(1.25))=0

We add all the numbers together, and all the variables

4x*3x+3*3x=0

Wy multiply elements

12x^2+9x=0

a = 12; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·12·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*12}=\frac{-18}{24}
=-3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*12}=\frac{0}{24}
=0
$