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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x+9)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


64x/128x^2+(-2x)/128x^2+(-6x)/128x^2-9=0

We multiply all the terms by the denominator


64x+(-2x)+(-6x)-9*128x^2=0

Wy multiply elements

-1152x^2+64x+(-2x)+(-6x)=0

We get rid of parentheses

-1152x^2+64x-2x-6x=0

We add all the numbers together, and all the variables

-1152x^2+56x=0

a = -1152; b = 56; c = 0;
Δ = b2-4ac
Δ = 562-4·(-1152)·0
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-56}{2*-1152}=\frac{-112}{-2304}
=7/144
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+56}{2*-1152}=\frac{0}{-2304}
=0
$