6+4/6x=9/10x

Solution for 6+4/6x=9/10x equation:

6+4/6x=9/10x

We move all terms to the left:

6+4/6x-(9/10x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 10x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4/6x-(+9/10x)+6=0

We get rid of parentheses

4/6x-9/10x+6=0

We calculate fractions


40x/60x^2+(-54x)/60x^2+6=0

We multiply all the terms by the denominator


40x+(-54x)+6*60x^2=0

Wy multiply elements

360x^2+40x+(-54x)=0

We get rid of parentheses

360x^2+40x-54x=0

We add all the numbers together, and all the variables

360x^2-14x=0

a = 360; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·360·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*360}=\frac{0}{720}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*360}=\frac{28}{720}
=7/180
$