5x+4/8x+5=34

Solution for 5x+4/8x+5=34 equation:

5x+4/8x+5=34

We move all terms to the left:

5x+4/8x+5-(34)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

5x+4/8x-29=0

We multiply all the terms by the denominator


5x*8x-29*8x+4=0

Wy multiply elements

40x^2-232x+4=0

a = 40; b = -232; c = +4;
Δ = b2-4ac
Δ = -2322-4·40·4
Δ = 53184
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:

$\sqrt{\Delta}=\sqrt{53184}=\sqrt{64*831}=\sqrt{64}*\sqrt{831}=8\sqrt{831}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-232)-8\sqrt{831}}{2*40}=\frac{232-8\sqrt{831}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-232)+8\sqrt{831}}{2*40}=\frac{232+8\sqrt{831}}{80}
$