1/3x-10=-4x=

Solution for 1/3x-10=-4x= equation:

1/3x-10=-4x=

We move all terms to the left:

1/3x-10-(-4x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/3x+4x-10=0

We multiply all the terms by the denominator


4x*3x-10*3x+1=0

Wy multiply elements

12x^2-30x+1=0

a = 12; b = -30; c = +1;
Δ = b2-4ac
Δ = -302-4·12·1
Δ = 852
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:

$\sqrt{\Delta}=\sqrt{852}=\sqrt{4*213}=\sqrt{4}*\sqrt{213}=2\sqrt{213}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{213}}{2*12}=\frac{30-2\sqrt{213}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{213}}{2*12}=\frac{30+2\sqrt{213}}{24}
$