4+4x=10+10/3x

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

4+4x=10+10/3x

We move all terms to the left:

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


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

12x^2-30x+12x-10=0

We add all the numbers together, and all the variables

12x^2-18x-10=0

a = 12; b = -18; c = -10;
Δ = b2-4ac
Δ = -182-4·12·(-10)
Δ = 804
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{804}=\sqrt{4*201}=\sqrt{4}*\sqrt{201}=2\sqrt{201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{201}}{2*12}=\frac{18-2\sqrt{201}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{201}}{2*12}=\frac{18+2\sqrt{201}}{24}
$