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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

15x^2-15x-12x+4=0

We add all the numbers together, and all the variables

15x^2-27x+4=0

a = 15; b = -27; c = +4;
Δ = b2-4ac
Δ = -272-4·15·4
Δ = 489
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-\sqrt{489}}{2*15}=\frac{27-\sqrt{489}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{489}}{2*15}=\frac{27+\sqrt{489}}{30}
$