-1/2x+4/5=3+1/9x

Solution for -1/2x+4/5=3+1/9x equation:

-1/2x+4/5=3+1/9x

We move all terms to the left:

-1/2x+4/5-(3+1/9x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 9x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-1/2x-(1/9x+3)+4/5=0

We get rid of parentheses

-1/2x-1/9x-3+4/5=0

We calculate fractions


648x^2/450x^2+(-225x)/450x^2+(-50x)/450x^2-3=0

We multiply all the terms by the denominator


648x^2+(-225x)+(-50x)-3*450x^2=0

Wy multiply elements

648x^2-1350x^2+(-225x)+(-50x)=0

We get rid of parentheses

648x^2-1350x^2-225x-50x=0

We add all the numbers together, and all the variables

-702x^2-275x=0

a = -702; b = -275; c = 0;
Δ = b2-4ac
Δ = -2752-4·(-702)·0
Δ = 75625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{75625}=275$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-275)-275}{2*-702}=\frac{0}{-1404}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-275)+275}{2*-702}=\frac{550}{-1404}
=-275/702
$