4/10x=2/3x-14

Solution for 4/10x=2/3x-14 equation:

4/10x=2/3x-14

We move all terms to the left:

4/10x-(2/3x-14)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 3x-14)!=0

x∈R


We get rid of parentheses

4/10x-2/3x+14=0

We calculate fractions


12x/30x^2+(-20x)/30x^2+14=0

We multiply all the terms by the denominator


12x+(-20x)+14*30x^2=0

Wy multiply elements

420x^2+12x+(-20x)=0

We get rid of parentheses

420x^2+12x-20x=0

We add all the numbers together, and all the variables

420x^2-8x=0

a = 420; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·420·0
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*420}=\frac{0}{840}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*420}=\frac{16}{840}
=2/105
$