9/4x+7/6=-3/2x

Solution for 9/4x+7/6=-3/2x equation:

9/4x+7/6=-3/2x

We move all terms to the left:

9/4x+7/6-(-3/2x)=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 get rid of parentheses

9/4x+3/2x+7/6=0

We calculate fractions


112x^2/288x^2+648x/288x^2+432x/288x^2=0

We multiply all the terms by the denominator


112x^2+648x+432x=0

We add all the numbers together, and all the variables

112x^2+1080x=0

a = 112; b = 1080; c = 0;
Δ = b2-4ac
Δ = 10802-4·112·0
Δ = 1166400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1166400}=1080$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1080)-1080}{2*112}=\frac{-2160}{224}
=-9+9/14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1080)+1080}{2*112}=\frac{0}{224}
=0
$