7x+31=8x-(1/3)(27x+3)

Solution for 7x+31=8x-(1/3)(27x+3) equation:

7x+31=8x-(1/3)(27x+3)

We move all terms to the left:

7x+31-(8x-(1/3)(27x+3))=0


Domain of the equation: 3)(27x+3))!=0

x∈R


We add all the numbers together, and all the variables

7x-(8x-(+1/3)(27x+3))+31=0

We multiply parentheses ..

-(8x-(+27x^2+1/3*3))+7x+31=0

We multiply all the terms by the denominator


-(8x-(+27x^2+1+7x*3*3))+31*3*3))=0


We calculate terms in parentheses: -(8x-(+27x^2+1+7x*3*3)), so:

8x-(+27x^2+1+7x*3*3)

determiningTheFunctionDomain
-(+27x^2+1+7x*3*3)+8x

We get rid of parentheses

-27x^2-7x*3*3+8x-1

We add all the numbers together, and all the variables

-27x^2+8x-7x*3*3-1

Wy multiply elements

-27x^2+8x-63x*3-1

Wy multiply elements

-27x^2+8x-189x-1

We add all the numbers together, and all the variables

-27x^2-181x-1

Back to the equation:

-(-27x^2-181x-1)


We add all the numbers together, and all the variables

-(-27x^2-181x-1)=0

We get rid of parentheses

27x^2+181x+1=0

a = 27; b = 181; c = +1;
Δ = b2-4ac
Δ = 1812-4·27·1
Δ = 32653
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(181)-\sqrt{32653}}{2*27}=\frac{-181-\sqrt{32653}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(181)+\sqrt{32653}}{2*27}=\frac{-181+\sqrt{32653}}{54}
$