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

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

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

We move all terms to the left:

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


Domain of the equation: 2x-15)!=0

x∈R


We add all the numbers together, and all the variables

2x-(1/2x-15)+3=0

We get rid of parentheses

2x-1/2x+15+3=0

We multiply all the terms by the denominator


2x*2x+15*2x+3*2x-1=0

Wy multiply elements

4x^2+30x+6x-1=0

We add all the numbers together, and all the variables

4x^2+36x-1=0

a = 4; b = 36; c = -1;
Δ = b2-4ac
Δ = 362-4·4·(-1)
Δ = 1312
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:

$\sqrt{\Delta}=\sqrt{1312}=\sqrt{16*82}=\sqrt{16}*\sqrt{82}=4\sqrt{82}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{82}}{2*4}=\frac{-36-4\sqrt{82}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{82}}{2*4}=\frac{-36+4\sqrt{82}}{8}
$