1/2x=-7/9x+3

Solution for 1/2x=-7/9x+3 equation:

1/2x=-7/9x+3

We move all terms to the left:

1/2x-(-7/9x+3)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 9x+3)!=0

x∈R


We get rid of parentheses

1/2x+7/9x-3=0

We calculate fractions


9x/18x^2+14x/18x^2-3=0

We multiply all the terms by the denominator


9x+14x-3*18x^2=0

We add all the numbers together, and all the variables

23x-3*18x^2=0

Wy multiply elements

-54x^2+23x=0

a = -54; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·(-54)·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-23}{2*-54}=\frac{-46}{-108}
=23/54
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*-54}=\frac{0}{-108}
=0
$