1/2x-75=x-15

Solution for 1/2x-75=x-15 equation:

1/2x-75=x-15

We move all terms to the left:

1/2x-75-(x-15)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-x+15-75=0

We multiply all the terms by the denominator


-x*2x+15*2x-75*2x+1=0

Wy multiply elements

-2x^2+30x-150x+1=0

We add all the numbers together, and all the variables

-2x^2-120x+1=0

a = -2; b = -120; c = +1;
Δ = b2-4ac
Δ = -1202-4·(-2)·1
Δ = 14408
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:

$\sqrt{\Delta}=\sqrt{14408}=\sqrt{4*3602}=\sqrt{4}*\sqrt{3602}=2\sqrt{3602}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-2\sqrt{3602}}{2*-2}=\frac{120-2\sqrt{3602}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+2\sqrt{3602}}{2*-2}=\frac{120+2\sqrt{3602}}{-4}
$