5/4x+3/2x=11/16

Solution for 5/4x+3/2x=11/16 equation:

5/4x+3/2x=11/16

We move all terms to the left:

5/4x+3/2x-(11/16)=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

5/4x+3/2x-(+11/16)=0

We get rid of parentheses

5/4x+3/2x-11/16=0

We calculate fractions


(-176x^2)/128x^2+160x/128x^2+192x/128x^2=0

We multiply all the terms by the denominator


(-176x^2)+160x+192x=0

We add all the numbers together, and all the variables

(-176x^2)+352x=0

We get rid of parentheses

-176x^2+352x=0

a = -176; b = 352; c = 0;
Δ = b2-4ac
Δ = 3522-4·(-176)·0
Δ = 123904
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{123904}=352$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(352)-352}{2*-176}=\frac{-704}{-352}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(352)+352}{2*-176}=\frac{0}{-352}
=0
$