3/4x-4/8x=9

Solution for 3/4x-4/8x=9 equation:

3/4x-4/8x=9

We move all terms to the left:

3/4x-4/8x-(9)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We calculate fractions


24x/32x^2+(-16x)/32x^2-9=0

We multiply all the terms by the denominator


24x+(-16x)-9*32x^2=0

Wy multiply elements

-288x^2+24x+(-16x)=0

We get rid of parentheses

-288x^2+24x-16x=0

We add all the numbers together, and all the variables

-288x^2+8x=0

a = -288; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-288)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-288}=\frac{-16}{-576}
=1/36
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-288}=\frac{0}{-576}
=0
$