1/2x-60=2+5x

Solution for 1/2x-60=2+5x equation:

1/2x-60=2+5x

We move all terms to the left:

1/2x-60-(2+5x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(5x+2)-60=0

We get rid of parentheses

1/2x-5x-2-60=0

We multiply all the terms by the denominator


-5x*2x-2*2x-60*2x+1=0

Wy multiply elements

-10x^2-4x-120x+1=0

We add all the numbers together, and all the variables

-10x^2-124x+1=0

a = -10; b = -124; c = +1;
Δ = b2-4ac
Δ = -1242-4·(-10)·1
Δ = 15416
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:

$\sqrt{\Delta}=\sqrt{15416}=\sqrt{4*3854}=\sqrt{4}*\sqrt{3854}=2\sqrt{3854}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-124)-2\sqrt{3854}}{2*-10}=\frac{124-2\sqrt{3854}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-124)+2\sqrt{3854}}{2*-10}=\frac{124+2\sqrt{3854}}{-20}
$