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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

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

We calculate fractions


648x^2/192x^2+480x/192x^2+(-160x)/192x^2=0

We multiply all the terms by the denominator


648x^2+480x+(-160x)=0

We get rid of parentheses

648x^2+480x-160x=0

We add all the numbers together, and all the variables

648x^2+320x=0

a = 648; b = 320; c = 0;
Δ = b2-4ac
Δ = 3202-4·648·0
Δ = 102400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{102400}=320$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(320)-320}{2*648}=\frac{-640}{1296}
=-40/81
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(320)+320}{2*648}=\frac{0}{1296}
=0
$