12+15x=1/2x-60

Solution for 12+15x=1/2x-60 equation:

12+15x=1/2x-60

We move all terms to the left:

12+15x-(1/2x-60)=0


Domain of the equation: 2x-60)!=0

x∈R


We get rid of parentheses

15x-1/2x+60+12=0

We multiply all the terms by the denominator


15x*2x+60*2x+12*2x-1=0

Wy multiply elements

30x^2+120x+24x-1=0

We add all the numbers together, and all the variables

30x^2+144x-1=0

a = 30; b = 144; c = -1;
Δ = b2-4ac
Δ = 1442-4·30·(-1)
Δ = 20856
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:

$\sqrt{\Delta}=\sqrt{20856}=\sqrt{4*5214}=\sqrt{4}*\sqrt{5214}=2\sqrt{5214}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-2\sqrt{5214}}{2*30}=\frac{-144-2\sqrt{5214}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+2\sqrt{5214}}{2*30}=\frac{-144+2\sqrt{5214}}{60}
$