3/4x+15/10=2/8x

Solution for 3/4x+15/10=2/8x equation:

3/4x+15/10=2/8x

We move all terms to the left:

3/4x+15/10-(2/8x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x-(+2/8x)+15/10=0

We get rid of parentheses

3/4x-2/8x+15/10=0

We calculate fractions


3840x^2/320x^2+240x/320x^2+(-80x)/320x^2=0

We multiply all the terms by the denominator


3840x^2+240x+(-80x)=0

We get rid of parentheses

3840x^2+240x-80x=0

We add all the numbers together, and all the variables

3840x^2+160x=0

a = 3840; b = 160; c = 0;
Δ = b2-4ac
Δ = 1602-4·3840·0
Δ = 25600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25600}=160$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(160)-160}{2*3840}=\frac{-320}{7680}
=-1/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(160)+160}{2*3840}=\frac{0}{7680}
=0
$