7/3x+5/4x=-27/16

Solution for 7/3x+5/4x=-27/16 equation:

7/3x+5/4x=-27/16

We move all terms to the left:

7/3x+5/4x-(-27/16)=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 get rid of parentheses

7/3x+5/4x+27/16=0

We calculate fractions


1296x^2/192x^2+448x/192x^2+240x/192x^2=0

We multiply all the terms by the denominator


1296x^2+448x+240x=0

We add all the numbers together, and all the variables

1296x^2+688x=0

a = 1296; b = 688; c = 0;
Δ = b2-4ac
Δ = 6882-4·1296·0
Δ = 473344
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{473344}=688$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(688)-688}{2*1296}=\frac{-1376}{2592}
=-43/81
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(688)+688}{2*1296}=\frac{0}{2592}
=0
$