72/5x=3/6x-4

Solution for 72/5x=3/6x-4 equation:

72/5x=3/6x-4

We move all terms to the left:

72/5x-(3/6x-4)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



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

x∈R


We get rid of parentheses

72/5x-3/6x+4=0

We calculate fractions


432x/30x^2+(-15x)/30x^2+4=0

We multiply all the terms by the denominator


432x+(-15x)+4*30x^2=0

Wy multiply elements

120x^2+432x+(-15x)=0

We get rid of parentheses

120x^2+432x-15x=0

We add all the numbers together, and all the variables

120x^2+417x=0

a = 120; b = 417; c = 0;
Δ = b2-4ac
Δ = 4172-4·120·0
Δ = 173889
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{173889}=417$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(417)-417}{2*120}=\frac{-834}{240}
=-3+19/40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(417)+417}{2*120}=\frac{0}{240}
=0
$