7/5x=2/10x+6

Solution for 7/5x=2/10x+6 equation:

7/5x=2/10x+6

We move all terms to the left:

7/5x-(2/10x+6)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x+6)!=0

x∈R


We get rid of parentheses

7/5x-2/10x-6=0

We calculate fractions


70x/50x^2+(-10x)/50x^2-6=0

We multiply all the terms by the denominator


70x+(-10x)-6*50x^2=0

Wy multiply elements

-300x^2+70x+(-10x)=0

We get rid of parentheses

-300x^2+70x-10x=0

We add all the numbers together, and all the variables

-300x^2+60x=0

a = -300; b = 60; c = 0;
Δ = b2-4ac
Δ = 602-4·(-300)·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-60}{2*-300}=\frac{-120}{-600}
=1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+60}{2*-300}=\frac{0}{-600}
=0
$