3/8x-29=1/2x-19

Solution for 3/8x-29=1/2x-19 equation:

3/8x-29=1/2x-19

We move all terms to the left:

3/8x-29-(1/2x-19)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 2x-19)!=0

x∈R


We get rid of parentheses

3/8x-1/2x+19-29=0

We calculate fractions


6x/16x^2+(-8x)/16x^2+19-29=0

We add all the numbers together, and all the variables

6x/16x^2+(-8x)/16x^2-10=0

We multiply all the terms by the denominator


6x+(-8x)-10*16x^2=0

Wy multiply elements

-160x^2+6x+(-8x)=0

We get rid of parentheses

-160x^2+6x-8x=0

We add all the numbers together, and all the variables

-160x^2-2x=0

a = -160; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-160)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-160}=\frac{0}{-320}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-160}=\frac{4}{-320}
=-1/80
$