x/3x+4=5x-10

Solution for x/3x+4=5x-10 equation:

x/3x+4=5x-10

We move all terms to the left:

x/3x+4-(5x-10)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

x/3x-5x+10+4=0

We multiply all the terms by the denominator


x-5x*3x+10*3x+4*3x=0

Wy multiply elements

-15x^2+x+30x+12x=0

We add all the numbers together, and all the variables

-15x^2+43x=0

a = -15; b = 43; c = 0;
Δ = b2-4ac
Δ = 432-4·(-15)·0
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(43)-43}{2*-15}=\frac{-86}{-30}
=2+13/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+43}{2*-15}=\frac{0}{-30}
=0
$