42=-6(-2a2+11)

Solution for 42=-6(-2a2+11) equation:

42=-6(-2a^2+11)

We move all terms to the left:

42-(-6(-2a^2+11))=0


We calculate terms in parentheses: -(-6(-2a^2+11)), so:

-6(-2a^2+11)

We multiply parentheses

12a^2-66

Back to the equation:

-(12a^2-66)


We get rid of parentheses

-12a^2+66+42=0

We add all the numbers together, and all the variables

-12a^2+108=0

a = -12; b = 0; c = +108;
Δ = b2-4ac
Δ = 02-4·(-12)·108
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-72}{2*-12}=\frac{-72}{-24}
=+3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+72}{2*-12}=\frac{72}{-24}
=-3
$