3x+5/4x=34

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Solution for 3x+5/4x=34 equation: 



3x+5/4x=34

We move all terms to the left:

3x+5/4x-(34)=0



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



We multiply all the terms by the denominator


3x*4x-34*4x+5=0

Wy multiply elements

12x^2-136x+5=0

a = 12; b = -136; c = +5;
Δ = b2-4ac
Δ = -1362-4·12·5
Δ = 18256
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:


$\sqrt{\Delta}=\sqrt{18256}=\sqrt{16*1141}=\sqrt{16}*\sqrt{1141}=4\sqrt{1141}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-136)-4\sqrt{1141}}{2*12}=\frac{136-4\sqrt{1141}}{24}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-136)+4\sqrt{1141}}{2*12}=\frac{136+4\sqrt{1141}}{24}
$

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