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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x-4)!=0

x∈R


We get rid of parentheses

7/4x+5/3x+4+2=0

We calculate fractions


21x/12x^2+20x/12x^2+4+2=0

We add all the numbers together, and all the variables

21x/12x^2+20x/12x^2+6=0

We multiply all the terms by the denominator


21x+20x+6*12x^2=0

We add all the numbers together, and all the variables

41x+6*12x^2=0

Wy multiply elements

72x^2+41x=0

a = 72; b = 41; c = 0;
Δ = b2-4ac
Δ = 412-4·72·0
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-41}{2*72}=\frac{-82}{144}
=-41/72
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+41}{2*72}=\frac{0}{144}
=0
$