6a(3a+1)-30=3(2a-4)

Solution for 6a(3a+1)-30=3(2a-4) equation:

6a(3a+1)-30=3(2a-4)

We move all terms to the left:

6a(3a+1)-30-(3(2a-4))=0

We multiply parentheses

18a^2+6a-(3(2a-4))-30=0


We calculate terms in parentheses: -(3(2a-4)), so:

3(2a-4)

We multiply parentheses

6a-12

Back to the equation:

-(6a-12)


We get rid of parentheses

18a^2+6a-6a+12-30=0

We add all the numbers together, and all the variables

18a^2-18=0

a = 18; b = 0; c = -18;
Δ = b2-4ac
Δ = 02-4·18·(-18)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36}{2*18}=\frac{-36}{36}
=-1
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36}{2*18}=\frac{36}{36}
=1
$