4/5x-4=6/3x-7

Solution for 4/5x-4=6/3x-7 equation:

4/5x-4=6/3x-7

We move all terms to the left:

4/5x-4-(6/3x-7)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x-7)!=0

x∈R


We get rid of parentheses

4/5x-6/3x+7-4=0

We calculate fractions


12x/15x^2+(-30x)/15x^2+7-4=0

We add all the numbers together, and all the variables

12x/15x^2+(-30x)/15x^2+3=0

We multiply all the terms by the denominator


12x+(-30x)+3*15x^2=0

Wy multiply elements

45x^2+12x+(-30x)=0

We get rid of parentheses

45x^2+12x-30x=0

We add all the numbers together, and all the variables

45x^2-18x=0

a = 45; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·45·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*45}=\frac{0}{90}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*45}=\frac{36}{90}
=2/5
$