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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x-5)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-16x)/108x^2+81x/108x^2+20x/108x^2+5=0

We multiply all the terms by the denominator


(-16x)+81x+20x+5*108x^2=0

We add all the numbers together, and all the variables

101x+(-16x)+5*108x^2=0

Wy multiply elements

540x^2+101x+(-16x)=0

We get rid of parentheses

540x^2+101x-16x=0

We add all the numbers together, and all the variables

540x^2+85x=0

a = 540; b = 85; c = 0;
Δ = b2-4ac
Δ = 852-4·540·0
Δ = 7225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7225}=85$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(85)-85}{2*540}=\frac{-170}{1080}
=-17/108
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(85)+85}{2*540}=\frac{0}{1080}
=0
$