-10=a+3/3a=

Solution for -10=a+3/3a= equation:

-10=a+3/3a=

We move all terms to the left:

-10-(a+3/3a)=0


Domain of the equation: 3a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

-(+a+3/3a)-10=0

We get rid of parentheses

-a-3/3a-10=0

We multiply all the terms by the denominator


-a*3a-10*3a-3=0

Wy multiply elements

-3a^2-30a-3=0

a = -3; b = -30; c = -3;
Δ = b2-4ac
Δ = -302-4·(-3)·(-3)
Δ = 864
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-12\sqrt{6}}{2*-3}=\frac{30-12\sqrt{6}}{-6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+12\sqrt{6}}{2*-3}=\frac{30+12\sqrt{6}}{-6}
$