4x+38/5x-16=0

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Solution for 4x+38/5x-16=0 equation: 



4x+38/5x-16=0



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



We multiply all the terms by the denominator


4x*5x-16*5x+38=0

Wy multiply elements

20x^2-80x+38=0

a = 20; b = -80; c = +38;
Δ = b2-4ac
Δ = -802-4·20·38
Δ = 3360
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:


$\sqrt{\Delta}=\sqrt{3360}=\sqrt{16*210}=\sqrt{16}*\sqrt{210}=4\sqrt{210}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-4\sqrt{210}}{2*20}=\frac{80-4\sqrt{210}}{40}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+4\sqrt{210}}{2*20}=\frac{80+4\sqrt{210}}{40}
$

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