3/2x-2/3+5/4x=-49/24

Solution for 3/2x-2/3+5/4x=-49/24 equation:

3/2x-2/3+5/4x=-49/24

We move all terms to the left:

3/2x-2/3+5/4x-(-49/24)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

3/2x+5/4x-2/3+49/24=0

We calculate fractions


(-1536x^2)/1728x^2+4704x^2/1728x^2+2592x/1728x^2+2160x/1728x^2=0

We multiply all the terms by the denominator


(-1536x^2)+4704x^2+2592x+2160x=0

We add all the numbers together, and all the variables

4704x^2+(-1536x^2)+4752x=0

We get rid of parentheses

4704x^2-1536x^2+4752x=0

We add all the numbers together, and all the variables

3168x^2+4752x=0

a = 3168; b = 4752; c = 0;
Δ = b2-4ac
Δ = 47522-4·3168·0
Δ = 22581504
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{22581504}=4752$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4752)-4752}{2*3168}=\frac{-9504}{6336}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4752)+4752}{2*3168}=\frac{0}{6336}
=0
$