.5x+(8/3)x=x+39

Solution for .5x+(8/3)x=x+39 equation:

.5x+(8/3)x=x+39

We move all terms to the left:

.5x+(8/3)x-(x+39)=0


Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

.5x+(+8/3)x-(x+39)=0

We multiply parentheses

8x^2+.5x-(x+39)=0

We get rid of parentheses

8x^2+.5x-x-39=0

We add all the numbers together, and all the variables

8x^2-0.5x-39=0

a = 8; b = -0.5; c = -39;
Δ = b2-4ac
Δ = -0.52-4·8·(-39)
Δ = 1248.25
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{-(-0.5)-\sqrt{1248.25}}{2*8}=\frac{0.5-\sqrt{1248.25}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.5)+\sqrt{1248.25}}{2*8}=\frac{0.5+\sqrt{1248.25}}{16}
$