4x+9x-8/8x=14/2

Solution for 4x+9x-8/8x=14/2 equation:

4x+9x-8/8x=14/2

We move all terms to the left:

4x+9x-8/8x-(14/2)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

4x+9x-8/8x-7=0

We add all the numbers together, and all the variables

13x-8/8x-7=0

We multiply all the terms by the denominator


13x*8x-7*8x-8=0

Wy multiply elements

104x^2-56x-8=0

a = 104; b = -56; c = -8;
Δ = b2-4ac
Δ = -562-4·104·(-8)
Δ = 6464
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6464}=\sqrt{64*101}=\sqrt{64}*\sqrt{101}=8\sqrt{101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-8\sqrt{101}}{2*104}=\frac{56-8\sqrt{101}}{208}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+8\sqrt{101}}{2*104}=\frac{56+8\sqrt{101}}{208}
$