-2+1/10x=7-4/5x

Solution for -2+1/10x=7-4/5x equation:

-2+1/10x=7-4/5x

We move all terms to the left:

-2+1/10x-(7-4/5x)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/10x-(-4/5x+7)-2=0

We get rid of parentheses

1/10x+4/5x-7-2=0

We calculate fractions


5x/50x^2+40x/50x^2-7-2=0

We add all the numbers together, and all the variables

5x/50x^2+40x/50x^2-9=0

We multiply all the terms by the denominator


5x+40x-9*50x^2=0

We add all the numbers together, and all the variables

45x-9*50x^2=0

Wy multiply elements

-450x^2+45x=0

a = -450; b = 45; c = 0;
Δ = b2-4ac
Δ = 452-4·(-450)·0
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-45}{2*-450}=\frac{-90}{-900}
=1/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+45}{2*-450}=\frac{0}{-900}
=0
$