8(5-x)=1/2x

Solution for 8(5-x)=1/2x equation:

8(5-x)=1/2x

We move all terms to the left:

8(5-x)-(1/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

8(-1x+5)-(+1/2x)=0

We multiply parentheses

-8x-(+1/2x)+40=0

We get rid of parentheses

-8x-1/2x+40=0

We multiply all the terms by the denominator


-8x*2x+40*2x-1=0

Wy multiply elements

-16x^2+80x-1=0

a = -16; b = 80; c = -1;
Δ = b2-4ac
Δ = 802-4·(-16)·(-1)
Δ = 6336
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:

$\sqrt{\Delta}=\sqrt{6336}=\sqrt{576*11}=\sqrt{576}*\sqrt{11}=24\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-24\sqrt{11}}{2*-16}=\frac{-80-24\sqrt{11}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+24\sqrt{11}}{2*-16}=\frac{-80+24\sqrt{11}}{-32}
$