10x+5x+1/2x=100

Solution for 10x+5x+1/2x=100 equation:

10x+5x+1/2x=100

We move all terms to the left:

10x+5x+1/2x-(100)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

15x+1/2x-100=0

We multiply all the terms by the denominator


15x*2x-100*2x+1=0

Wy multiply elements

30x^2-200x+1=0

a = 30; b = -200; c = +1;
Δ = b2-4ac
Δ = -2002-4·30·1
Δ = 39880
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:

$\sqrt{\Delta}=\sqrt{39880}=\sqrt{4*9970}=\sqrt{4}*\sqrt{9970}=2\sqrt{9970}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-2\sqrt{9970}}{2*30}=\frac{200-2\sqrt{9970}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+2\sqrt{9970}}{2*30}=\frac{200+2\sqrt{9970}}{60}
$