9-1/4x=1/2x-3

Solution for 9-1/4x=1/2x-3 equation:

9-1/4x=1/2x-3

We move all terms to the left:

9-1/4x-(1/2x-3)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x-3)!=0

x∈R


We get rid of parentheses

-1/4x-1/2x+3+9=0

We calculate fractions


(-2x)/8x^2+(-4x)/8x^2+3+9=0

We add all the numbers together, and all the variables

(-2x)/8x^2+(-4x)/8x^2+12=0

We multiply all the terms by the denominator


(-2x)+(-4x)+12*8x^2=0

Wy multiply elements

96x^2+(-2x)+(-4x)=0

We get rid of parentheses

96x^2-2x-4x=0

We add all the numbers together, and all the variables

96x^2-6x=0

a = 96; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·96·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*96}=\frac{0}{192}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*96}=\frac{12}{192}
=1/16
$