5/2x-1-4/3x+2=-7

Solution for 5/2x-1-4/3x+2=-7 equation:

5/2x-1-4/3x+2=-7

We move all terms to the left:

5/2x-1-4/3x+2-(-7)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

5/2x-4/3x+8=0

We calculate fractions


15x/6x^2+(-8x)/6x^2+8=0

We multiply all the terms by the denominator


15x+(-8x)+8*6x^2=0

Wy multiply elements

48x^2+15x+(-8x)=0

We get rid of parentheses

48x^2+15x-8x=0

We add all the numbers together, and all the variables

48x^2+7x=0

a = 48; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·48·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*48}=\frac{-14}{96}
=-7/48
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*48}=\frac{0}{96}
=0
$