Y=2x^2-6x-10

Solution for Y=2x^2-6x-10 equation:

=2Y^2-6Y-10

We move all terms to the left:

-(2Y^2-6Y-10)=0

We get rid of parentheses

-2Y^2+6Y+10=0

a = -2; b = 6; c = +10;
Δ = b2-4ac
Δ = 62-4·(-2)·10
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{29}}{2*-2}=\frac{-6-2\sqrt{29}}{-4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{29}}{2*-2}=\frac{-6+2\sqrt{29}}{-4}
$