1/2x-1/5-2/3x=-41/180

Solution for 1/2x-1/5-2/3x=-41/180 equation:

1/2x-1/5-2/3x=-41/180

We move all terms to the left:

1/2x-1/5-2/3x-(-41/180)=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-2/3x-1/5+41/180=0

We calculate fractions


(-3240x^2)/27000x^2+3690x^2/27000x^2+13500x/27000x^2+(-18000x)/27000x^2=0

We multiply all the terms by the denominator


(-3240x^2)+3690x^2+13500x+(-18000x)=0

We add all the numbers together, and all the variables

3690x^2+(-3240x^2)+13500x+(-18000x)=0

We get rid of parentheses

3690x^2-3240x^2+13500x-18000x=0

We add all the numbers together, and all the variables

450x^2-4500x=0

a = 450; b = -4500; c = 0;
Δ = b2-4ac
Δ = -45002-4·450·0
Δ = 20250000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20250000}=4500$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4500)-4500}{2*450}=\frac{0}{900}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4500)+4500}{2*450}=\frac{9000}{900}
=10
$