0.5+4/3x=x+10

Solution for 0.5+4/3x=x+10 equation:

0.5+4/3x=x+10

We move all terms to the left:

0.5+4/3x-(x+10)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

4/3x-x-10+0.5=0

We multiply all the terms by the denominator


-x*3x-10*3x+(0.5)*3x+4=0

We multiply parentheses

-x*3x-10*3x+1.5x+4=0

Wy multiply elements

-3x^2-30x+1.5x+4=0

We add all the numbers together, and all the variables

-3x^2-28.5x+4=0

a = -3; b = -28.5; c = +4;
Δ = b2-4ac
Δ = -28.52-4·(-3)·4
Δ = 860.25
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{-(-28.5)-\sqrt{860.25}}{2*-3}=\frac{28.5-\sqrt{860.25}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28.5)+\sqrt{860.25}}{2*-3}=\frac{28.5+\sqrt{860.25}}{-6}
$