-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 add all the numbers together, and all the variables

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

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+1

Wy multiply elements

-15a^2+540a*1+1

Wy multiply elements

-15a^2+540a+1

Back to the equation:

-(-15a^2+540a+1)


We add all the numbers together, and all the variables

-(-15a^2+540a+1)=0

We get rid of parentheses

15a^2-540a-1=0

a = 15; b = -540; c = -1;
Δ = b2-4ac
Δ = -5402-4·15·(-1)
Δ = 291660
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:

$\sqrt{\Delta}=\sqrt{291660}=\sqrt{4*72915}=\sqrt{4}*\sqrt{72915}=2\sqrt{72915}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-540)-2\sqrt{72915}}{2*15}=\frac{540-2\sqrt{72915}}{30}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-540)+2\sqrt{72915}}{2*15}=\frac{540+2\sqrt{72915}}{30}
$