80-1/3x=0.5x-30

Solution for 80-1/3x=0.5x-30 equation:

80-1/3x=0.5x-30

We move all terms to the left:

80-1/3x-(0.5x-30)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

-1/3x-0.5x+30+80=0

We multiply all the terms by the denominator


-(0.5x)*3x+30*3x+80*3x-1=0

We add all the numbers together, and all the variables

-(+0.5x)*3x+30*3x+80*3x-1=0

We multiply parentheses

-0x^2+30*3x+80*3x-1=0

Wy multiply elements

-0x^2+90x+240x-1=0

We add all the numbers together, and all the variables

-1x^2+330x-1=0

a = -1; b = 330; c = -1;
Δ = b2-4ac
Δ = 3302-4·(-1)·(-1)
Δ = 108896
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:

$\sqrt{\Delta}=\sqrt{108896}=\sqrt{16*6806}=\sqrt{16}*\sqrt{6806}=4\sqrt{6806}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(330)-4\sqrt{6806}}{2*-1}=\frac{-330-4\sqrt{6806}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(330)+4\sqrt{6806}}{2*-1}=\frac{-330+4\sqrt{6806}}{-2}
$