Y=6x^2-24x+13

Solution for Y=6x^2-24x+13 equation:

=6Y^2-24Y+13

We move all terms to the left:

-(6Y^2-24Y+13)=0

We get rid of parentheses

-6Y^2+24Y-13=0

a = -6; b = 24; c = -13;
Δ = b2-4ac
Δ = 242-4·(-6)·(-13)
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{66}}{2*-6}=\frac{-24-2\sqrt{66}}{-12}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{66}}{2*-6}=\frac{-24+2\sqrt{66}}{-12}
$