8+7/10x=6-1/5x

Solution for 8+7/10x=6-1/5x equation:

8+7/10x=6-1/5x

We move all terms to the left:

8+7/10x-(6-1/5x)=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

7/10x-(-1/5x+6)+8=0

We get rid of parentheses

7/10x+1/5x-6+8=0

We calculate fractions


35x/50x^2+10x/50x^2-6+8=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

45x+2*50x^2=0

Wy multiply elements

100x^2+45x=0

a = 100; b = 45; c = 0;
Δ = b2-4ac
Δ = 452-4·100·0
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*100}=\frac{-90}{200}
=-9/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+45}{2*100}=\frac{0}{200}
=0
$