2x+9/4x=34

Solution for 2x+9/4x=34 equation:

2x+9/4x=34

We move all terms to the left:

2x+9/4x-(34)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


2x*4x-34*4x+9=0

Wy multiply elements

8x^2-136x+9=0

a = 8; b = -136; c = +9;
Δ = b2-4ac
Δ = -1362-4·8·9
Δ = 18208
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:

$\sqrt{\Delta}=\sqrt{18208}=\sqrt{16*1138}=\sqrt{16}*\sqrt{1138}=4\sqrt{1138}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-136)-4\sqrt{1138}}{2*8}=\frac{136-4\sqrt{1138}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-136)+4\sqrt{1138}}{2*8}=\frac{136+4\sqrt{1138}}{16}
$