2+1/5x+4x=23

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Solution for 2+1/5x+4x=23 equation: 



2+1/5x+4x=23

We move all terms to the left:

2+1/5x+4x-(23)=0



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



We add all the numbers together, and all the variables

4x+1/5x-21=0

We multiply all the terms by the denominator


4x*5x-21*5x+1=0

Wy multiply elements

20x^2-105x+1=0

a = 20; b = -105; c = +1;
Δ = b2-4ac
Δ = -1052-4·20·1
Δ = 10945
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-105)-\sqrt{10945}}{2*20}=\frac{105-\sqrt{10945}}{40}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+\sqrt{10945}}{2*20}=\frac{105+\sqrt{10945}}{40}
$

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