x/3(2x)+x-2x=100

Solution for x/3(2x)+x-2x=100 equation:

x/3(2x)+x-2x=100

We move all terms to the left:

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


Domain of the equation: 32x!=0

x!=0/32

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+x/32x-100=0

We multiply all the terms by the denominator


-1x*32x+x-100*32x=0

We add all the numbers together, and all the variables

x-1x*32x-100*32x=0

Wy multiply elements

-32x^2+x-3200x=0

We add all the numbers together, and all the variables

-32x^2-3199x=0

a = -32; b = -3199; c = 0;
Δ = b2-4ac
Δ = -31992-4·(-32)·0
Δ = 10233601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10233601}=3199$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3199)-3199}{2*-32}=\frac{0}{-64}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3199)+3199}{2*-32}=\frac{6398}{-64}
=-99+31/32
$