1/18x+7/9x=33

Solution for 1/18x+7/9x=33 equation:

1/18x+7/9x=33

We move all terms to the left:

1/18x+7/9x-(33)=0


Domain of the equation: 18x!=0

x!=0/18

x!=0

x∈R



Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We calculate fractions


9x/162x^2+126x/162x^2-33=0

We multiply all the terms by the denominator


9x+126x-33*162x^2=0

We add all the numbers together, and all the variables

135x-33*162x^2=0

Wy multiply elements

-5346x^2+135x=0

a = -5346; b = 135; c = 0;
Δ = b2-4ac
Δ = 1352-4·(-5346)·0
Δ = 18225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{18225}=135$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(135)-135}{2*-5346}=\frac{-270}{-10692}
=5/198
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(135)+135}{2*-5346}=\frac{0}{-10692}
=0
$