-102=6(-3x2)

Solution for -102=6(-3x2) equation:

-102=6(-3x^2)

We move all terms to the left:

-102-(6(-3x^2))=0


We calculate terms in parentheses: -(6(-3x^2)), so:

6(-3x^2)

We multiply parentheses

-18x^2

Back to the equation:

-(-18x^2)


We get rid of parentheses

18x^2-102=0

a = 18; b = 0; c = -102;
Δ = b2-4ac
Δ = 02-4·18·(-102)
Δ = 7344
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{7344}=\sqrt{144*51}=\sqrt{144}*\sqrt{51}=12\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{51}}{2*18}=\frac{0-12\sqrt{51}}{36}
=-\frac{12\sqrt{51}}{36}
=-\frac{\sqrt{51}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{51}}{2*18}=\frac{0+12\sqrt{51}}{36}
=\frac{12\sqrt{51}}{36}
=\frac{\sqrt{51}}{3}
$