5/9x+2/3x-1=35

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Solution for 5/9x+2/3x-1=35 equation: 



5/9x+2/3x-1=35

We move all terms to the left:

5/9x+2/3x-1-(35)=0



Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R





Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



We add all the numbers together, and all the variables

5/9x+2/3x-36=0

We calculate fractions


15x/27x^2+18x/27x^2-36=0

We multiply all the terms by the denominator


15x+18x-36*27x^2=0

We add all the numbers together, and all the variables

33x-36*27x^2=0

Wy multiply elements

-972x^2+33x=0

a = -972; b = 33; c = 0;
Δ = b2-4ac
Δ = 332-4·(-972)·0
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-33}{2*-972}=\frac{-66}{-1944}
=11/324
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+33}{2*-972}=\frac{0}{-1944}
=0
$

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