1/2x+1/3x=-25/18

Solution for 1/2x+1/3x=-25/18 equation:

1/2x+1/3x=-25/18

We move all terms to the left:

1/2x+1/3x-(-25/18)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/2x+1/3x+25/18=0

We calculate fractions


450x^2/108x^2+54x/108x^2+36x/108x^2=0

We multiply all the terms by the denominator


450x^2+54x+36x=0

We add all the numbers together, and all the variables

450x^2+90x=0

a = 450; b = 90; c = 0;
Δ = b2-4ac
Δ = 902-4·450·0
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-90}{2*450}=\frac{-180}{900}
=-1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+90}{2*450}=\frac{0}{900}
=0
$