40=(-1/3)(9x+30)+2

Solution for 40=(-1/3)(9x+30)+2 equation:

40=(-1/3)(9x+30)+2

We move all terms to the left:

40-((-1/3)(9x+30)+2)=0


Domain of the equation: 3)(9x+30)+2)!=0

x∈R


We multiply parentheses ..

-((-9x^2-1/3*30)+2)+40=0

We multiply all the terms by the denominator


-((-9x^2-1+40*3*30)+2)=0


We calculate terms in parentheses: -((-9x^2-1+40*3*30)+2), so:

(-9x^2-1+40*3*30)+2

We get rid of parentheses

-9x^2-1+2+40*3*30

We add all the numbers together, and all the variables

-9x^2+3601

Back to the equation:

-(-9x^2+3601)


We get rid of parentheses

9x^2-3601=0

a = 9; b = 0; c = -3601;
Δ = b2-4ac
Δ = 02-4·9·(-3601)
Δ = 129636
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:

$\sqrt{\Delta}=\sqrt{129636}=\sqrt{36*3601}=\sqrt{36}*\sqrt{3601}=6\sqrt{3601}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{3601}}{2*9}=\frac{0-6\sqrt{3601}}{18}
=-\frac{6\sqrt{3601}}{18}
=-\frac{\sqrt{3601}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{3601}}{2*9}=\frac{0+6\sqrt{3601}}{18}
=\frac{6\sqrt{3601}}{18}
=\frac{\sqrt{3601}}{3}
$