1/2x+1/4x+1/5=19/20

Solution for 1/2x+1/4x+1/5=19/20 equation:

1/2x+1/4x+1/5=19/20

We move all terms to the left:

1/2x+1/4x+1/5-(19/20)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x+1/4x+1/5-(+19/20)=0

We get rid of parentheses

1/2x+1/4x+1/5-19/20=0

We calculate fractions


(-3040x^2)/4000x^2+640x^2/4000x^2+2000x/4000x^2+1000x/4000x^2=0

We multiply all the terms by the denominator


(-3040x^2)+640x^2+2000x+1000x=0

We add all the numbers together, and all the variables

640x^2+(-3040x^2)+3000x=0

We get rid of parentheses

640x^2-3040x^2+3000x=0

We add all the numbers together, and all the variables

-2400x^2+3000x=0

a = -2400; b = 3000; c = 0;
Δ = b2-4ac
Δ = 30002-4·(-2400)·0
Δ = 9000000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9000000}=3000$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3000)-3000}{2*-2400}=\frac{-6000}{-4800}
=1+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3000)+3000}{2*-2400}=\frac{0}{-4800}
=0
$