-2(6a-1)=-(-5/3)(3a+15)+6

Solution for -2(6a-1)=-(-5/3)(3a+15)+6 equation:

-2(6a-1)=-(-5/3)(3a+15)+6

We move all terms to the left:

-2(6a-1)-(-(-5/3)(3a+15)+6)=0


Domain of the equation: 3)(3a+15)+6)!=0

a∈R


We multiply parentheses

-12a-(-(-5/3)(3a+15)+6)+2=0

We multiply parentheses ..

-(-(-15a^2-5/3*15)+6)-12a+2=0

We multiply all the terms by the denominator


-(-(-15a^2-5-12a*3*15)+6)+2*3*15)+6)=0


We calculate terms in parentheses: -(-(-15a^2-5-12a*3*15)+6), so:

-(-15a^2-5-12a*3*15)+6

We get rid of parentheses

15a^2+12a*3*15+5+6

We add all the numbers together, and all the variables

15a^2+12a*3*15+11

Wy multiply elements

15a^2+540a*1+11

Wy multiply elements

15a^2+540a+11

Back to the equation:

-(15a^2+540a+11)


We add all the numbers together, and all the variables

-(15a^2+540a+11)=0

We get rid of parentheses

-15a^2-540a-11=0

a = -15; b = -540; c = -11;
Δ = b2-4ac
Δ = -5402-4·(-15)·(-11)
Δ = 290940
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:

$\sqrt{\Delta}=\sqrt{290940}=\sqrt{4*72735}=\sqrt{4}*\sqrt{72735}=2\sqrt{72735}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-540)-2\sqrt{72735}}{2*-15}=\frac{540-2\sqrt{72735}}{-30}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-540)+2\sqrt{72735}}{2*-15}=\frac{540+2\sqrt{72735}}{-30}
$