-7/4x-3/2x=13/16

Solution for -7/4x-3/2x=13/16 equation:

-7/4x-3/2x=13/16

We move all terms to the left:

-7/4x-3/2x-(13/16)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-7/4x-3/2x-(+13/16)=0

We get rid of parentheses

-7/4x-3/2x-13/16=0

We calculate fractions


(-208x^2)/128x^2+(-224x)/128x^2+(-192x)/128x^2=0

We multiply all the terms by the denominator


(-208x^2)+(-224x)+(-192x)=0

We get rid of parentheses

-208x^2-224x-192x=0

We add all the numbers together, and all the variables

-208x^2-416x=0

a = -208; b = -416; c = 0;
Δ = b2-4ac
Δ = -4162-4·(-208)·0
Δ = 173056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{173056}=416$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-416)-416}{2*-208}=\frac{0}{-416}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-416)+416}{2*-208}=\frac{832}{-416}
=-2
$