1/2x+3/10x=100

Solution for 1/2x+3/10x=100 equation:

1/2x+3/10x=100

We move all terms to the left:

1/2x+3/10x-(100)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We calculate fractions


10x/20x^2+6x/20x^2-100=0

We multiply all the terms by the denominator


10x+6x-100*20x^2=0

We add all the numbers together, and all the variables

16x-100*20x^2=0

Wy multiply elements

-2000x^2+16x=0

a = -2000; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-2000)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-2000}=\frac{-32}{-4000}
=1/125
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-2000}=\frac{0}{-4000}
=0
$