x/6x+4=3x+10

Solution for x/6x+4=3x+10 equation:

x/6x+4=3x+10

We move all terms to the left:

x/6x+4-(3x+10)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

x/6x-3x-10+4=0

We multiply all the terms by the denominator


x-3x*6x-10*6x+4*6x=0

Wy multiply elements

-18x^2+x-60x+24x=0

We add all the numbers together, and all the variables

-18x^2-35x=0

a = -18; b = -35; c = 0;
Δ = b2-4ac
Δ = -352-4·(-18)·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-35}{2*-18}=\frac{0}{-36}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+35}{2*-18}=\frac{70}{-36}
=-1+17/18
$