-x+100=1/2x-28

Solution for -x+100=1/2x-28 equation:

-x+100=1/2x-28

We move all terms to the left:

-x+100-(1/2x-28)=0


Domain of the equation: 2x-28)!=0

x∈R


We add all the numbers together, and all the variables

-1x-(1/2x-28)+100=0

We get rid of parentheses

-1x-1/2x+28+100=0

We multiply all the terms by the denominator


-1x*2x+28*2x+100*2x-1=0

Wy multiply elements

-2x^2+56x+200x-1=0

We add all the numbers together, and all the variables

-2x^2+256x-1=0

a = -2; b = 256; c = -1;
Δ = b2-4ac
Δ = 2562-4·(-2)·(-1)
Δ = 65528
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:

$\sqrt{\Delta}=\sqrt{65528}=\sqrt{4*16382}=\sqrt{4}*\sqrt{16382}=2\sqrt{16382}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(256)-2\sqrt{16382}}{2*-2}=\frac{-256-2\sqrt{16382}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(256)+2\sqrt{16382}}{2*-2}=\frac{-256+2\sqrt{16382}}{-4}
$