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

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

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

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 30x!=0

x!=0/30

x!=0

x∈R


We add all the numbers together, and all the variables

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

We calculate fractions


540x^2/4500x^2+(-3750x)/4500x^2+(-1050x)/4500x^2+52=0

We multiply all the terms by the denominator


540x^2+(-3750x)+(-1050x)+52*4500x^2=0

Wy multiply elements

540x^2+234000x^2+(-3750x)+(-1050x)=0

We get rid of parentheses

540x^2+234000x^2-3750x-1050x=0

We add all the numbers together, and all the variables

234540x^2-4800x=0

a = 234540; b = -4800; c = 0;
Δ = b2-4ac
Δ = -48002-4·234540·0
Δ = 23040000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{23040000}=4800$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4800)-4800}{2*234540}=\frac{0}{469080}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4800)+4800}{2*234540}=\frac{9600}{469080}
=80/3909
$