13/20x+4/3-1/4x=11/16

Solution for 13/20x+4/3-1/4x=11/16 equation:

13/20x+4/3-1/4x=11/16

We move all terms to the left:

13/20x+4/3-1/4x-(11/16)=0


Domain of the equation: 20x!=0

x!=0/20

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

13/20x-1/4x+4/3-(+11/16)=0

We get rid of parentheses

13/20x-1/4x+4/3-11/16=0

We calculate fractions


(-10560x^2)/11520x^2+20480x^2/11520x^2+7488x/11520x^2+(-2880x)/11520x^2=0

We multiply all the terms by the denominator


(-10560x^2)+20480x^2+7488x+(-2880x)=0

We add all the numbers together, and all the variables

20480x^2+(-10560x^2)+7488x+(-2880x)=0

We get rid of parentheses

20480x^2-10560x^2+7488x-2880x=0

We add all the numbers together, and all the variables

9920x^2+4608x=0

a = 9920; b = 4608; c = 0;
Δ = b2-4ac
Δ = 46082-4·9920·0
Δ = 21233664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{21233664}=4608$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4608)-4608}{2*9920}=\frac{-9216}{19840}
=-72/155
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4608)+4608}{2*9920}=\frac{0}{19840}
=0
$