1/3x+1/4x=7/20

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Solution for 1/3x+1/4x=7/20 equation: 



1/3x+1/4x=7/20

We move all terms to the left:

1/3x+1/4x-(7/20)=0



Domain of the equation: 3x!=0

x!=0/3

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

1/3x+1/4x-(+7/20)=0

We get rid of parentheses

1/3x+1/4x-7/20=0

We calculate fractions


(-336x^2)/480x^2+160x/480x^2+120x/480x^2=0

We multiply all the terms by the denominator


(-336x^2)+160x+120x=0

We add all the numbers together, and all the variables

(-336x^2)+280x=0

We get rid of parentheses

-336x^2+280x=0

a = -336; b = 280; c = 0;
Δ = b2-4ac
Δ = 2802-4·(-336)·0
Δ = 78400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{78400}=280$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(280)-280}{2*-336}=\frac{-560}{-672}
=5/6
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(280)+280}{2*-336}=\frac{0}{-672}
=0
$

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