1/3x=20x+10

Solution for 1/3x=20x+10 equation:

1/3x=20x+10

We move all terms to the left:

1/3x-(20x+10)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/3x-20x-10=0

We multiply all the terms by the denominator


-20x*3x-10*3x+1=0

Wy multiply elements

-60x^2-30x+1=0

a = -60; b = -30; c = +1;
Δ = b2-4ac
Δ = -302-4·(-60)·1
Δ = 1140
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:

$\sqrt{\Delta}=\sqrt{1140}=\sqrt{4*285}=\sqrt{4}*\sqrt{285}=2\sqrt{285}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{285}}{2*-60}=\frac{30-2\sqrt{285}}{-120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{285}}{2*-60}=\frac{30+2\sqrt{285}}{-120}
$