21.9-6x=1/2x-8

Solution for 21.9-6x=1/2x-8 equation:

21.9-6x=1/2x-8

We move all terms to the left:

21.9-6x-(1/2x-8)=0


Domain of the equation: 2x-8)!=0

x∈R


We get rid of parentheses

-6x-1/2x+8+21.9=0

We multiply all the terms by the denominator


-6x*2x+8*2x+(21.9)*2x-1=0

We multiply parentheses

-6x*2x+8*2x+43.8x-1=0

Wy multiply elements

-12x^2+16x+43.8x-1=0

We add all the numbers together, and all the variables

-12x^2+59.8x-1=0

a = -12; b = 59.8; c = -1;
Δ = b2-4ac
Δ = 59.82-4·(-12)·(-1)
Δ = 3528.04
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(59.8)-\sqrt{3528.04}}{2*-12}=\frac{-59.8-\sqrt{3528.04}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(59.8)+\sqrt{3528.04}}{2*-12}=\frac{-59.8+\sqrt{3528.04}}{-24}
$