8/3x-10=x

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

8/3x-10=x

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+8/3x-10=0

We multiply all the terms by the denominator


-1x*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 = 996
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:

$\sqrt{\Delta}=\sqrt{996}=\sqrt{4*249}=\sqrt{4}*\sqrt{249}=2\sqrt{249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{249}}{2*-3}=\frac{30-2\sqrt{249}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{249}}{2*-3}=\frac{30+2\sqrt{249}}{-6}
$