-5/9x+1=2/3x-10

Solution for -5/9x+1=2/3x-10 equation:

-5/9x+1=2/3x-10

We move all terms to the left:

-5/9x+1-(2/3x-10)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 3x-10)!=0

x∈R


We get rid of parentheses

-5/9x-2/3x+10+1=0

We calculate fractions


(-15x)/27x^2+(-18x)/27x^2+10+1=0

We add all the numbers together, and all the variables

(-15x)/27x^2+(-18x)/27x^2+11=0

We multiply all the terms by the denominator


(-15x)+(-18x)+11*27x^2=0

Wy multiply elements

297x^2+(-15x)+(-18x)=0

We get rid of parentheses

297x^2-15x-18x=0

We add all the numbers together, and all the variables

297x^2-33x=0

a = 297; b = -33; c = 0;
Δ = b2-4ac
Δ = -332-4·297·0
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*297}=\frac{0}{594}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+33}{2*297}=\frac{66}{594}
=1/9
$