1/3x+30=6x

Solution for 1/3x+30=6x equation:

1/3x+30=6x

We move all terms to the left:

1/3x+30-(6x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-6x+1/3x+30=0

We multiply all the terms by the denominator


-6x*3x+30*3x+1=0

Wy multiply elements

-18x^2+90x+1=0

a = -18; b = 90; c = +1;
Δ = b2-4ac
Δ = 902-4·(-18)·1
Δ = 8172
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:

$\sqrt{\Delta}=\sqrt{8172}=\sqrt{36*227}=\sqrt{36}*\sqrt{227}=6\sqrt{227}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-6\sqrt{227}}{2*-18}=\frac{-90-6\sqrt{227}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+6\sqrt{227}}{2*-18}=\frac{-90+6\sqrt{227}}{-36}
$