1/5x+1/2(2x)=18

Solution for 1/5x+1/2(2x)=18 equation:

1/5x+1/2(2x)=18

We move all terms to the left:

1/5x+1/2(2x)-(18)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 22x!=0

x!=0/22

x!=0

x∈R


We calculate fractions


22x/110x^2+5x/110x^2-18=0

We multiply all the terms by the denominator


22x+5x-18*110x^2=0

We add all the numbers together, and all the variables

27x-18*110x^2=0

Wy multiply elements

-1980x^2+27x=0

a = -1980; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·(-1980)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*-1980}=\frac{-54}{-3960}
=3/220
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*-1980}=\frac{0}{-3960}
=0
$