-10=2/3x+x

Solution for -10=2/3x+x equation:

-10=2/3x+x

We move all terms to the left:

-10-(2/3x+x)=0


Domain of the equation: 3x+x)!=0

x∈R


We add all the numbers together, and all the variables

-(+x+2/3x)-10=0

We get rid of parentheses

-x-2/3x-10=0

We multiply all the terms by the denominator


-x*3x-10*3x-2=0

Wy multiply elements

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

a = -3; b = -30; c = -2;
Δ = b2-4ac
Δ = -302-4·(-3)·(-2)
Δ = 876
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:

$\sqrt{\Delta}=\sqrt{876}=\sqrt{4*219}=\sqrt{4}*\sqrt{219}=2\sqrt{219}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{219}}{2*-3}=\frac{30-2\sqrt{219}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{219}}{2*-3}=\frac{30+2\sqrt{219}}{-6}
$