-1/4x+5/6=9/2x

Solution for -1/4x+5/6=9/2x equation:

-1/4x+5/6=9/2x

We move all terms to the left:

-1/4x+5/6-(9/2x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-1/4x-(+9/2x)+5/6=0

We get rid of parentheses

-1/4x-9/2x+5/6=0

We calculate fractions


80x^2/288x^2+(-72x)/288x^2+(-1296x)/288x^2=0

We multiply all the terms by the denominator


80x^2+(-72x)+(-1296x)=0

We get rid of parentheses

80x^2-72x-1296x=0

We add all the numbers together, and all the variables

80x^2-1368x=0

a = 80; b = -1368; c = 0;
Δ = b2-4ac
Δ = -13682-4·80·0
Δ = 1871424
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1871424}=1368$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1368)-1368}{2*80}=\frac{0}{160}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1368)+1368}{2*80}=\frac{2736}{160}
=17+1/10
$