Y=6x^2+18x-21

Solution for Y=6x^2+18x-21 equation:

=6Y^2+18Y-21

We move all terms to the left:

-(6Y^2+18Y-21)=0

We get rid of parentheses

-6Y^2-18Y+21=0

a = -6; b = -18; c = +21;
Δ = b2-4ac
Δ = -182-4·(-6)·21
Δ = 828
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{828}=\sqrt{36*23}=\sqrt{36}*\sqrt{23}=6\sqrt{23}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{23}}{2*-6}=\frac{18-6\sqrt{23}}{-12}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{23}}{2*-6}=\frac{18+6\sqrt{23}}{-12}
$