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

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

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

We move all terms to the left:

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


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

We multiply parentheses

0x^2-x*3x-5*3x+4=0

Wy multiply elements

0x^2-3x^2-15x+4=0

We add all the numbers together, and all the variables

-2x^2-15x+4=0

a = -2; b = -15; c = +4;
Δ = b2-4ac
Δ = -152-4·(-2)·4
Δ = 257
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{-(-15)-\sqrt{257}}{2*-2}=\frac{15-\sqrt{257}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{257}}{2*-2}=\frac{15+\sqrt{257}}{-4}
$