-3/2x+9/4x=21/16

Solution for -3/2x+9/4x=21/16 equation:

-3/2x+9/4x=21/16

We move all terms to the left:

-3/2x+9/4x-(21/16)=0


Domain of the equation: 2x!=0

x!=0/2

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

-3/2x+9/4x-(+21/16)=0

We get rid of parentheses

-3/2x+9/4x-21/16=0

We calculate fractions


(-672x^2)/128x^2+(-192x)/128x^2+288x/128x^2=0

We multiply all the terms by the denominator


(-672x^2)+(-192x)+288x=0

We add all the numbers together, and all the variables

(-672x^2)+288x+(-192x)=0

We get rid of parentheses

-672x^2+288x-192x=0

We add all the numbers together, and all the variables

-672x^2+96x=0

a = -672; b = 96; c = 0;
Δ = b2-4ac
Δ = 962-4·(-672)·0
Δ = 9216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9216}=96$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-96}{2*-672}=\frac{-192}{-1344}
=1/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+96}{2*-672}=\frac{0}{-1344}
=0
$