1/2(10x)+4x=108

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Solution for 1/2(10x)+4x=108 equation: 



1/2(10x)+4x=108

We move all terms to the left:

1/2(10x)+4x-(108)=0



Domain of the equation: 210x!=0

x!=0/210

x!=0

x∈R



We add all the numbers together, and all the variables

4x+1/210x-108=0

We multiply all the terms by the denominator


4x*210x-108*210x+1=0

Wy multiply elements

840x^2-22680x+1=0

a = 840; b = -22680; c = +1;
Δ = b2-4ac
Δ = -226802-4·840·1
Δ = 514379040
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:


$\sqrt{\Delta}=\sqrt{514379040}=\sqrt{16*32148690}=\sqrt{16}*\sqrt{32148690}=4\sqrt{32148690}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22680)-4\sqrt{32148690}}{2*840}=\frac{22680-4\sqrt{32148690}}{1680}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22680)+4\sqrt{32148690}}{2*840}=\frac{22680+4\sqrt{32148690}}{1680}
$

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