Y=2x^2+10x-6

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

=2Y^2+10Y-6

We move all terms to the left:

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

We get rid of parentheses

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

a = -2; b = -10; c = +6;
Δ = b2-4ac
Δ = -102-4·(-2)·6
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{37}}{2*-2}=\frac{10-2\sqrt{37}}{-4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{37}}{2*-2}=\frac{10+2\sqrt{37}}{-4}
$