-4/3x-5/4=5/2x-1

Solution for -4/3x-5/4=5/2x-1 equation:

-4/3x-5/4=5/2x-1

We move all terms to the left:

-4/3x-5/4-(5/2x-1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x-1)!=0

x∈R


We get rid of parentheses

-4/3x-5/2x+1-5/4=0

We calculate fractions


(-60x^2)/96x^2+(-128x)/96x^2+(-240x)/96x^2+1=0

We multiply all the terms by the denominator


(-60x^2)+(-128x)+(-240x)+1*96x^2=0

Wy multiply elements

(-60x^2)+96x^2+(-128x)+(-240x)=0

We get rid of parentheses

-60x^2+96x^2-128x-240x=0

We add all the numbers together, and all the variables

36x^2-368x=0

a = 36; b = -368; c = 0;
Δ = b2-4ac
Δ = -3682-4·36·0
Δ = 135424
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{135424}=368$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-368)-368}{2*36}=\frac{0}{72}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-368)+368}{2*36}=\frac{736}{72}
=10+2/9
$