3/4x+3/2x=-18

Solution for 3/4x+3/2x=-18 equation:

3/4x+3/2x=-18

We move all terms to the left:

3/4x+3/2x-(-18)=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+18=0

We calculate fractions


6x/8x^2+12x/8x^2+18=0

We multiply all the terms by the denominator


6x+12x+18*8x^2=0

We add all the numbers together, and all the variables

18x+18*8x^2=0

Wy multiply elements

144x^2+18x=0

a = 144; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·144·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*144}=\frac{-36}{288}
=-1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*144}=\frac{0}{288}
=0
$