5/3x-x=10

Solution for 5/3x-x=10 equation:

5/3x-x=10

We move all terms to the left:

5/3x-x-(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

-1x+5/3x-10=0

We multiply all the terms by the denominator


-1x*3x-10*3x+5=0

Wy multiply elements

-3x^2-30x+5=0

a = -3; b = -30; c = +5;
Δ = b2-4ac
Δ = -302-4·(-3)·5
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-8\sqrt{15}}{2*-3}=\frac{30-8\sqrt{15}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+8\sqrt{15}}{2*-3}=\frac{30+8\sqrt{15}}{-6}
$