1/5x+2=6-7/10x

Solution for 1/5x+2=6-7/10x equation:

1/5x+2=6-7/10x

We move all terms to the left:

1/5x+2-(6-7/10x)=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

1/5x-(-7/10x+6)+2=0

We get rid of parentheses

1/5x+7/10x-6+2=0

We calculate fractions


10x/50x^2+35x/50x^2-6+2=0

We add all the numbers together, and all the variables

10x/50x^2+35x/50x^2-4=0

We multiply all the terms by the denominator


10x+35x-4*50x^2=0

We add all the numbers together, and all the variables

45x-4*50x^2=0

Wy multiply elements

-200x^2+45x=0

a = -200; b = 45; c = 0;
Δ = b2-4ac
Δ = 452-4·(-200)·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*-200}=\frac{-90}{-400}
=9/40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+45}{2*-200}=\frac{0}{-400}
=0
$