x+8/3x=-10

Solution for x+8/3x=-10 equation:

x+8/3x=-10

We move all terms to the left:

x+8/3x-(-10)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

x+8/3x+10=0

We multiply all the terms by the denominator


x*3x+10*3x+8=0

Wy multiply elements

3x^2+30x+8=0

a = 3; b = 30; c = +8;
Δ = b2-4ac
Δ = 302-4·3·8
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{-(30)-2\sqrt{201}}{2*3}=\frac{-30-2\sqrt{201}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{201}}{2*3}=\frac{-30+2\sqrt{201}}{6}
$