1/2x+17=-2x-13

Solution for 1/2x+17=-2x-13 equation:

1/2x+17=-2x-13

We move all terms to the left:

1/2x+17-(-2x-13)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x+2x+13+17=0

We multiply all the terms by the denominator


2x*2x+13*2x+17*2x+1=0

Wy multiply elements

4x^2+26x+34x+1=0

We add all the numbers together, and all the variables

4x^2+60x+1=0

a = 4; b = 60; c = +1;
Δ = b2-4ac
Δ = 602-4·4·1
Δ = 3584
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:

$\sqrt{\Delta}=\sqrt{3584}=\sqrt{256*14}=\sqrt{256}*\sqrt{14}=16\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-16\sqrt{14}}{2*4}=\frac{-60-16\sqrt{14}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+16\sqrt{14}}{2*4}=\frac{-60+16\sqrt{14}}{8}
$