7x-22=-(1/3)(9x+6)

Solution for 7x-22=-(1/3)(9x+6) equation:

7x-22=-(1/3)(9x+6)

We move all terms to the left:

7x-22-(-(1/3)(9x+6))=0


Domain of the equation: 3)(9x+6))!=0

x∈R


We add all the numbers together, and all the variables

7x-(-(+1/3)(9x+6))-22=0

We multiply parentheses ..

-(-(+9x^2+1/3*6))+7x-22=0

We multiply all the terms by the denominator


-(-(+9x^2+1+7x*3*6))-22*3*6))=0


We calculate terms in parentheses: -(-(+9x^2+1+7x*3*6)), so:

-(+9x^2+1+7x*3*6)

We get rid of parentheses

-9x^2-7x*3*6-1

Wy multiply elements

-9x^2-126x*6-1

Wy multiply elements

-9x^2-756x-1

Back to the equation:

-(-9x^2-756x-1)


We add all the numbers together, and all the variables

-(-9x^2-756x-1)=0

We get rid of parentheses

9x^2+756x+1=0

a = 9; b = 756; c = +1;
Δ = b2-4ac
Δ = 7562-4·9·1
Δ = 571500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{571500}=\sqrt{900*635}=\sqrt{900}*\sqrt{635}=30\sqrt{635}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(756)-30\sqrt{635}}{2*9}=\frac{-756-30\sqrt{635}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(756)+30\sqrt{635}}{2*9}=\frac{-756+30\sqrt{635}}{18}
$