X+4=-5/2x-17

Solution for X+4=-5/2x-17 equation:

X+4=-5/2X-17

We move all terms to the left:

X+4-(-5/2X-17)=0


Domain of the equation: 2X-17)!=0

X∈R


We get rid of parentheses

X+5/2X+17+4=0

We multiply all the terms by the denominator


X*2X+17*2X+4*2X+5=0

Wy multiply elements

2X^2+34X+8X+5=0

We add all the numbers together, and all the variables

2X^2+42X+5=0

a = 2; b = 42; c = +5;
Δ = b2-4ac
Δ = 422-4·2·5
Δ = 1724
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:

$\sqrt{\Delta}=\sqrt{1724}=\sqrt{4*431}=\sqrt{4}*\sqrt{431}=2\sqrt{431}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{431}}{2*2}=\frac{-42-2\sqrt{431}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{431}}{2*2}=\frac{-42+2\sqrt{431}}{4}
$