6/5x-1=6-6/10x

Solution for 6/5x-1=6-6/10x equation:

6/5x-1=6-6/10x

We move all terms to the left:

6/5x-1-(6-6/10x)=0


Domain of the equation: 5x!=0

x!=0/5

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

6/5x-(-6/10x+6)-1=0

We get rid of parentheses

6/5x+6/10x-6-1=0

We calculate fractions


60x/50x^2+30x/50x^2-6-1=0

We add all the numbers together, and all the variables

60x/50x^2+30x/50x^2-7=0

We multiply all the terms by the denominator


60x+30x-7*50x^2=0

We add all the numbers together, and all the variables

90x-7*50x^2=0

Wy multiply elements

-350x^2+90x=0

a = -350; b = 90; c = 0;
Δ = b2-4ac
Δ = 902-4·(-350)·0
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-90}{2*-350}=\frac{-180}{-700}
=9/35
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+90}{2*-350}=\frac{0}{-700}
=0
$