5/4x+1/6x=-17/24

Solution for 5/4x+1/6x=-17/24 equation:

5/4x+1/6x=-17/24

We move all terms to the left:

5/4x+1/6x-(-17/24)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

5/4x+1/6x+17/24=0

We calculate fractions


2448x^2/1152x^2+1440x/1152x^2+192x/1152x^2=0

We multiply all the terms by the denominator


2448x^2+1440x+192x=0

We add all the numbers together, and all the variables

2448x^2+1632x=0

a = 2448; b = 1632; c = 0;
Δ = b2-4ac
Δ = 16322-4·2448·0
Δ = 2663424
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2663424}=1632$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1632)-1632}{2*2448}=\frac{-3264}{4896}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1632)+1632}{2*2448}=\frac{0}{4896}
=0
$