3/4x+3/2x=9/8

Solution for 3/4x+3/2x=9/8 equation:

3/4x+3/2x=9/8

We move all terms to the left:

3/4x+3/2x-(9/8)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x+3/2x-(+9/8)=0

We get rid of parentheses

3/4x+3/2x-9/8=0

We calculate fractions


(-144x^2)/512x^2+384x/512x^2+768x/512x^2=0

We multiply all the terms by the denominator


(-144x^2)+384x+768x=0

We add all the numbers together, and all the variables

(-144x^2)+1152x=0

We get rid of parentheses

-144x^2+1152x=0

a = -144; b = 1152; c = 0;
Δ = b2-4ac
Δ = 11522-4·(-144)·0
Δ = 1327104
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1327104}=1152$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1152)-1152}{2*-144}=\frac{-2304}{-288}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1152)+1152}{2*-144}=\frac{0}{-288}
=0
$