-1/3x+30=-x=10

Solution for -1/3x+30=-x=10 equation:

-1/3x+30=-x=10

We move all terms to the left:

-1/3x+30-(-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

-1/3x-(-1x)+30=0

We get rid of parentheses

-1/3x+1x+30=0

We multiply all the terms by the denominator


1x*3x+30*3x-1=0

Wy multiply elements

3x^2+90x-1=0

a = 3; b = 90; c = -1;
Δ = b2-4ac
Δ = 902-4·3·(-1)
Δ = 8112
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:

$\sqrt{\Delta}=\sqrt{8112}=\sqrt{2704*3}=\sqrt{2704}*\sqrt{3}=52\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-52\sqrt{3}}{2*3}=\frac{-90-52\sqrt{3}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+52\sqrt{3}}{2*3}=\frac{-90+52\sqrt{3}}{6}
$