1/3x+20=4x

Solution for 1/3x+20=4x equation:

1/3x+20=4x

We move all terms to the left:

1/3x+20-(4x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-4x+1/3x+20=0

We multiply all the terms by the denominator


-4x*3x+20*3x+1=0

Wy multiply elements

-12x^2+60x+1=0

a = -12; b = 60; c = +1;
Δ = b2-4ac
Δ = 602-4·(-12)·1
Δ = 3648
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:

$\sqrt{\Delta}=\sqrt{3648}=\sqrt{64*57}=\sqrt{64}*\sqrt{57}=8\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-8\sqrt{57}}{2*-12}=\frac{-60-8\sqrt{57}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+8\sqrt{57}}{2*-12}=\frac{-60+8\sqrt{57}}{-24}
$