1/3x+1/5=7/6(-7-3)

Solution for 1/3x+1/5=7/6(-7-3) equation:

1/3x+1/5=7/6(-7-3)

We move all terms to the left:

1/3x+1/5-(7/6(-7-3))=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

1/3x+1/5-(7/6(-10))=0

We calculate fractions


108x^2/540x^2+()/540x^2+(-(7*3x*5)/540x^2=0

We add all the numbers together, and all the variables

108x^2/540x^2+()/540x^2+(-(+7*3x*5)/540x^2=0

We multiply all the terms by the denominator


108x^2+(-(+7*3x*5)+()=0


We calculate terms in parentheses: +(-(+7*3x*5)+(), so:

-(+7*3x*5)+(

We add all the numbers together, and all the variables

-(+7*3x*5)

We get rid of parentheses

-7*3x*5

Wy multiply elements

-105x*5

Wy multiply elements

-525x

Back to the equation:

+(-525x)


We get rid of parentheses

108x^2-525x=0

a = 108; b = -525; c = 0;
Δ = b2-4ac
Δ = -5252-4·108·0
Δ = 275625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{275625}=525$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-525)-525}{2*108}=\frac{0}{216}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-525)+525}{2*108}=\frac{1050}{216}
=4+31/36
$