1/59x+60=2/3x-2

Solution for 1/59x+60=2/3x-2 equation:

1/59x+60=2/3x-2

We move all terms to the left:

1/59x+60-(2/3x-2)=0


Domain of the equation: 59x!=0

x!=0/59

x!=0

x∈R



Domain of the equation: 3x-2)!=0

x∈R


We get rid of parentheses

1/59x-2/3x+2+60=0

We calculate fractions


3x/177x^2+(-118x)/177x^2+2+60=0

We add all the numbers together, and all the variables

3x/177x^2+(-118x)/177x^2+62=0

We multiply all the terms by the denominator


3x+(-118x)+62*177x^2=0

Wy multiply elements

10974x^2+3x+(-118x)=0

We get rid of parentheses

10974x^2+3x-118x=0

We add all the numbers together, and all the variables

10974x^2-115x=0

a = 10974; b = -115; c = 0;
Δ = b2-4ac
Δ = -1152-4·10974·0
Δ = 13225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{13225}=115$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-115)-115}{2*10974}=\frac{0}{21948}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-115)+115}{2*10974}=\frac{230}{21948}
=115/10974
$