3/4x-8=23/24x-5

Solution for 3/4x-8=23/24x-5 equation:

3/4x-8=23/24x-5

We move all terms to the left:

3/4x-8-(23/24x-5)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 24x-5)!=0

x∈R


We get rid of parentheses

3/4x-23/24x+5-8=0

We calculate fractions


72x/96x^2+(-92x)/96x^2+5-8=0

We add all the numbers together, and all the variables

72x/96x^2+(-92x)/96x^2-3=0

We multiply all the terms by the denominator


72x+(-92x)-3*96x^2=0

Wy multiply elements

-288x^2+72x+(-92x)=0

We get rid of parentheses

-288x^2+72x-92x=0

We add all the numbers together, and all the variables

-288x^2-20x=0

a = -288; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·(-288)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*-288}=\frac{0}{-576}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*-288}=\frac{40}{-576}
=-5/72
$