5/6x-1/2=3/8x+1

Solution for 5/6x-1/2=3/8x+1 equation:

5/6x-1/2=3/8x+1

We move all terms to the left:

5/6x-1/2-(3/8x+1)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 8x+1)!=0

x∈R


We get rid of parentheses

5/6x-3/8x-1-1/2=0

We calculate fractions


(-384x^2)/192x^2+160x/192x^2+(-72x)/192x^2-1=0

We multiply all the terms by the denominator


(-384x^2)+160x+(-72x)-1*192x^2=0

Wy multiply elements

(-384x^2)-192x^2+160x+(-72x)=0

We get rid of parentheses

-384x^2-192x^2+160x-72x=0

We add all the numbers together, and all the variables

-576x^2+88x=0

a = -576; b = 88; c = 0;
Δ = b2-4ac
Δ = 882-4·(-576)·0
Δ = 7744
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7744}=88$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(88)-88}{2*-576}=\frac{-176}{-1152}
=11/72
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(88)+88}{2*-576}=\frac{0}{-1152}
=0
$