9/4x+1/8+7/8x=14

Solution for 9/4x+1/8+7/8x=14 equation:

9/4x+1/8+7/8x=14

We move all terms to the left:

9/4x+1/8+7/8x-(14)=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


determiningTheFunctionDomain
9/4x+7/8x-14+1/8=0

We calculate fractions


4608x/2048x^2+28x/2048x^2+4x/2048x^2-14=0

We multiply all the terms by the denominator


4608x+28x+4x-14*2048x^2=0

We add all the numbers together, and all the variables

4640x-14*2048x^2=0

Wy multiply elements

-28672x^2+4640x=0

a = -28672; b = 4640; c = 0;
Δ = b2-4ac
Δ = 46402-4·(-28672)·0
Δ = 21529600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{21529600}=4640$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4640)-4640}{2*-28672}=\frac{-9280}{-57344}
=145/896
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4640)+4640}{2*-28672}=\frac{0}{-57344}
=0
$