-5/6x-7/30+1/5x=-52

Solution for -5/6x-7/30+1/5x=-52 equation:

-5/6x-7/30+1/5x=-52

We move all terms to the left:

-5/6x-7/30+1/5x-(-52)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-5/6x+1/5x+52-7/30=0

We calculate fractions


(-1050x^2)/2700x^2+(-2250x)/2700x^2+540x/2700x^2+52=0

We multiply all the terms by the denominator


(-1050x^2)+(-2250x)+540x+52*2700x^2=0

We add all the numbers together, and all the variables

(-1050x^2)+540x+(-2250x)+52*2700x^2=0

Wy multiply elements

(-1050x^2)+140400x^2+540x+(-2250x)=0

We get rid of parentheses

-1050x^2+140400x^2+540x-2250x=0

We add all the numbers together, and all the variables

139350x^2-1710x=0

a = 139350; b = -1710; c = 0;
Δ = b2-4ac
Δ = -17102-4·139350·0
Δ = 2924100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2924100}=1710$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1710)-1710}{2*139350}=\frac{0}{278700}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1710)+1710}{2*139350}=\frac{3420}{278700}
=57/4645
$