(6/5)x=30+x

Solution for (6/5)x=30+x equation:

(6/5)x=30+x

We move all terms to the left:

(6/5)x-(30+x)=0


Domain of the equation: 5)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+6/5)x-(x+30)=0

We multiply parentheses

6x^2-(x+30)=0

We get rid of parentheses

6x^2-x-30=0

We add all the numbers together, and all the variables

6x^2-1x-30=0

a = 6; b = -1; c = -30;
Δ = b2-4ac
Δ = -12-4·6·(-30)
Δ = 721
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{721}}{2*6}=\frac{1-\sqrt{721}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{721}}{2*6}=\frac{1+\sqrt{721}}{12}
$