6/4x-4=10/3x+5

Solution for 6/4x-4=10/3x+5 equation:

6/4x-4=10/3x+5

We move all terms to the left:

6/4x-4-(10/3x+5)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x+5)!=0

x∈R


We get rid of parentheses

6/4x-10/3x-5-4=0

We calculate fractions


18x/12x^2+(-40x)/12x^2-5-4=0

We add all the numbers together, and all the variables

18x/12x^2+(-40x)/12x^2-9=0

We multiply all the terms by the denominator


18x+(-40x)-9*12x^2=0

Wy multiply elements

-108x^2+18x+(-40x)=0

We get rid of parentheses

-108x^2+18x-40x=0

We add all the numbers together, and all the variables

-108x^2-22x=0

a = -108; b = -22; c = 0;
Δ = b2-4ac
Δ = -222-4·(-108)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-22}{2*-108}=\frac{0}{-216}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+22}{2*-108}=\frac{44}{-216}
=-11/54
$