0.5x+(4/3)x=x+5

Solution for 0.5x+(4/3)x=x+5 equation:

0.5x+(4/3)x=x+5

We move all terms to the left:

0.5x+(4/3)x-(x+5)=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

0.5x+(+4/3)x-(x+5)=0

We multiply parentheses

4x^2+0.5x-(x+5)=0

We get rid of parentheses

4x^2+0.5x-x-5=0

We add all the numbers together, and all the variables

4x^2-0.5x-5=0

a = 4; b = -0.5; c = -5;
Δ = b2-4ac
Δ = -0.52-4·4·(-5)
Δ = 80.25
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{80.25}}{2*4}=\frac{0.5-\sqrt{80.25}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.5)+\sqrt{80.25}}{2*4}=\frac{0.5+\sqrt{80.25}}{8}
$