23/4x+11/3x=24

Solution for 23/4x+11/3x=24 equation:

23/4x+11/3x=24

We move all terms to the left:

23/4x+11/3x-(24)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


69x/12x^2+44x/12x^2-24=0

We multiply all the terms by the denominator


69x+44x-24*12x^2=0

We add all the numbers together, and all the variables

113x-24*12x^2=0

Wy multiply elements

-288x^2+113x=0

a = -288; b = 113; c = 0;
Δ = b2-4ac
Δ = 1132-4·(-288)·0
Δ = 12769
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12769}=113$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(113)-113}{2*-288}=\frac{-226}{-576}
=113/288
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(113)+113}{2*-288}=\frac{0}{-576}
=0
$