5-5x=5/2x+16

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

5-5x=5/2x+16

We move all terms to the left:

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


Domain of the equation: 2x+16)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-10x^2-32x+10x-5=0

We add all the numbers together, and all the variables

-10x^2-22x-5=0

a = -10; b = -22; c = -5;
Δ = b2-4ac
Δ = -222-4·(-10)·(-5)
Δ = 284
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:

$\sqrt{\Delta}=\sqrt{284}=\sqrt{4*71}=\sqrt{4}*\sqrt{71}=2\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{71}}{2*-10}=\frac{22-2\sqrt{71}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{71}}{2*-10}=\frac{22+2\sqrt{71}}{-20}
$