2/3x+10=4/10x

Solution for 2/3x+10=4/10x equation:

2/3x+10=4/10x

We move all terms to the left:

2/3x+10-(4/10x)=0


Domain of the equation: 3x!=0

x!=0/3

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

2/3x-(+4/10x)+10=0

We get rid of parentheses

2/3x-4/10x+10=0

We calculate fractions


20x/30x^2+(-12x)/30x^2+10=0

We multiply all the terms by the denominator


20x+(-12x)+10*30x^2=0

Wy multiply elements

300x^2+20x+(-12x)=0

We get rid of parentheses

300x^2+20x-12x=0

We add all the numbers together, and all the variables

300x^2+8x=0

a = 300; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·300·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*300}=\frac{-16}{600}
=-2/75
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*300}=\frac{0}{600}
=0
$