(5/3)x-2=x+6

Solution for (5/3)x-2=x+6 equation:

(5/3)x-2=x+6

We move all terms to the left:

(5/3)x-2-(x+6)=0


Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+5/3)x-(x+6)-2=0

We multiply parentheses

5x^2-(x+6)-2=0

We get rid of parentheses

5x^2-x-6-2=0

We add all the numbers together, and all the variables

5x^2-1x-8=0

a = 5; b = -1; c = -8;
Δ = b2-4ac
Δ = -12-4·5·(-8)
Δ = 161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{161}}{2*5}=\frac{1-\sqrt{161}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{161}}{2*5}=\frac{1+\sqrt{161}}{10}
$