1/2x+3/5=2/8x+9

Solution for 1/2x+3/5=2/8x+9 equation:

1/2x+3/5=2/8x+9

We move all terms to the left:

1/2x+3/5-(2/8x+9)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 8x+9)!=0

x∈R


We get rid of parentheses

1/2x-2/8x-9+3/5=0

We calculate fractions


384x^2/400x^2+200x/400x^2+(-100x)/400x^2-9=0

We multiply all the terms by the denominator


384x^2+200x+(-100x)-9*400x^2=0

Wy multiply elements

384x^2-3600x^2+200x+(-100x)=0

We get rid of parentheses

384x^2-3600x^2+200x-100x=0

We add all the numbers together, and all the variables

-3216x^2+100x=0

a = -3216; b = 100; c = 0;
Δ = b2-4ac
Δ = 1002-4·(-3216)·0
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-100}{2*-3216}=\frac{-200}{-6432}
=25/804
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+100}{2*-3216}=\frac{0}{-6432}
=0
$