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 = 684
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:

$\sqrt{\Delta}=\sqrt{684}=\sqrt{36*19}=\sqrt{36}*\sqrt{19}=6\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-6\sqrt{19}}{2*-10}=\frac{22-6\sqrt{19}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+6\sqrt{19}}{2*-10}=\frac{22+6\sqrt{19}}{-20}
$