-4/9x+7=-7/18x+9

Solution for -4/9x+7=-7/18x+9 equation:

-4/9x+7=-7/18x+9

We move all terms to the left:

-4/9x+7-(-7/18x+9)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 18x+9)!=0

x∈R


We get rid of parentheses

-4/9x+7/18x-9+7=0

We calculate fractions


(-72x)/162x^2+63x/162x^2-9+7=0

We add all the numbers together, and all the variables

(-72x)/162x^2+63x/162x^2-2=0

We multiply all the terms by the denominator


(-72x)+63x-2*162x^2=0

We add all the numbers together, and all the variables

63x+(-72x)-2*162x^2=0

Wy multiply elements

-324x^2+63x+(-72x)=0

We get rid of parentheses

-324x^2+63x-72x=0

We add all the numbers together, and all the variables

-324x^2-9x=0

a = -324; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·(-324)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*-324}=\frac{0}{-648}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*-324}=\frac{18}{-648}
=-1/36
$