0.6x-2=14-11/3x

Solution for 0.6x-2=14-11/3x equation:

0.6x-2=14-11/3x

We move all terms to the left:

0.6x-2-(14-11/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

0.6x-(-11/3x+14)-2=0

We get rid of parentheses

0.6x+11/3x-14-2=0

We multiply all the terms by the denominator


(0.6x)*3x-14*3x-2*3x+11=0

We add all the numbers together, and all the variables

(+0.6x)*3x-14*3x-2*3x+11=0

We multiply parentheses

0x^2-14*3x-2*3x+11=0

Wy multiply elements

0x^2-42x-6x+11=0

We add all the numbers together, and all the variables

x^2-48x+11=0

a = 1; b = -48; c = +11;
Δ = b2-4ac
Δ = -482-4·1·11
Δ = 2260
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:

$\sqrt{\Delta}=\sqrt{2260}=\sqrt{4*565}=\sqrt{4}*\sqrt{565}=2\sqrt{565}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-2\sqrt{565}}{2*1}=\frac{48-2\sqrt{565}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+2\sqrt{565}}{2*1}=\frac{48+2\sqrt{565}}{2}
$