2/3x-1/2=4/5x-10

Solution for 2/3x-1/2=4/5x-10 equation:

2/3x-1/2=4/5x-10

We move all terms to the left:

2/3x-1/2-(4/5x-10)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x-10)!=0

x∈R


We get rid of parentheses

2/3x-4/5x+10-1/2=0

We calculate fractions


(-75x^2)/60x^2+40x/60x^2+(-48x)/60x^2+10=0

We multiply all the terms by the denominator


(-75x^2)+40x+(-48x)+10*60x^2=0

Wy multiply elements

(-75x^2)+600x^2+40x+(-48x)=0

We get rid of parentheses

-75x^2+600x^2+40x-48x=0

We add all the numbers together, and all the variables

525x^2-8x=0

a = 525; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·525·0
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*525}=\frac{0}{1050}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*525}=\frac{16}{1050}
=8/525
$