10-3/5x=8-1/2x

Solution for 10-3/5x=8-1/2x equation:

10-3/5x=8-1/2x

We move all terms to the left:

10-3/5x-(8-1/2x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-3/5x-(-1/2x+8)+10=0

We get rid of parentheses

-3/5x+1/2x-8+10=0

We calculate fractions


(-6x)/10x^2+5x/10x^2-8+10=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


(-6x)+5x+2*10x^2=0

We add all the numbers together, and all the variables

5x+(-6x)+2*10x^2=0

Wy multiply elements

20x^2+5x+(-6x)=0

We get rid of parentheses

20x^2+5x-6x=0

We add all the numbers together, and all the variables

20x^2-1x=0

a = 20; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·20·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*20}=\frac{0}{40}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*20}=\frac{2}{40}
=1/20
$