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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 4x-6)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


12x/20x^2+(-15x)/20x^2+6+4=0

We add all the numbers together, and all the variables

12x/20x^2+(-15x)/20x^2+10=0

We multiply all the terms by the denominator


12x+(-15x)+10*20x^2=0

Wy multiply elements

200x^2+12x+(-15x)=0

We get rid of parentheses

200x^2+12x-15x=0

We add all the numbers together, and all the variables

200x^2-3x=0

a = 200; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·200·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*200}=\frac{0}{400}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*200}=\frac{6}{400}
=3/200
$