-3x=1/3x+10

Solution for -3x=1/3x+10 equation:

-3x=1/3x+10

We move all terms to the left:

-3x-(1/3x+10)=0


Domain of the equation: 3x+10)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-9x^2-30x-1=0

a = -9; b = -30; c = -1;
Δ = b2-4ac
Δ = -302-4·(-9)·(-1)
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-12\sqrt{6}}{2*-9}=\frac{30-12\sqrt{6}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+12\sqrt{6}}{2*-9}=\frac{30+12\sqrt{6}}{-18}
$