10+7/10x=6/5x-10

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

10+7/10x=6/5x-10

We move all terms to the left:

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


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 5x-10)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


35x/50x^2+(-60x)/50x^2+10+10=0

We add all the numbers together, and all the variables

35x/50x^2+(-60x)/50x^2+20=0

We multiply all the terms by the denominator


35x+(-60x)+20*50x^2=0

Wy multiply elements

1000x^2+35x+(-60x)=0

We get rid of parentheses

1000x^2+35x-60x=0

We add all the numbers together, and all the variables

1000x^2-25x=0

a = 1000; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·1000·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-25}{2*1000}=\frac{0}{2000}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*1000}=\frac{50}{2000}
=1/40
$