5/2x+6=x-16

Solution for 5/2x+6=x-16 equation:

5/2x+6=x-16

We move all terms to the left:

5/2x+6-(x-16)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

5/2x-x+16+6=0

We multiply all the terms by the denominator


-x*2x+16*2x+6*2x+5=0

Wy multiply elements

-2x^2+32x+12x+5=0

We add all the numbers together, and all the variables

-2x^2+44x+5=0

a = -2; b = 44; c = +5;
Δ = b2-4ac
Δ = 442-4·(-2)·5
Δ = 1976
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:

$\sqrt{\Delta}=\sqrt{1976}=\sqrt{4*494}=\sqrt{4}*\sqrt{494}=2\sqrt{494}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-2\sqrt{494}}{2*-2}=\frac{-44-2\sqrt{494}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+2\sqrt{494}}{2*-2}=\frac{-44+2\sqrt{494}}{-4}
$