2/3x=1/5x+45

Solution for 2/3x=1/5x+45 equation:

2/3x=1/5x+45

We move all terms to the left:

2/3x-(1/5x+45)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x+45)!=0

x∈R


We get rid of parentheses

2/3x-1/5x-45=0

We calculate fractions


10x/15x^2+(-3x)/15x^2-45=0

We multiply all the terms by the denominator


10x+(-3x)-45*15x^2=0

Wy multiply elements

-675x^2+10x+(-3x)=0

We get rid of parentheses

-675x^2+10x-3x=0

We add all the numbers together, and all the variables

-675x^2+7x=0

a = -675; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-675)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-675}=\frac{-14}{-1350}
=7/675
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-675}=\frac{0}{-1350}
=0
$