Y=2x2+4x-3

Solution for Y=2x2+4x-3 equation:

=2Y^2+4Y-3

We move all terms to the left:

-(2Y^2+4Y-3)=0

We get rid of parentheses

-2Y^2-4Y+3=0

a = -2; b = -4; c = +3;
Δ = b2-4ac
Δ = -42-4·(-2)·3
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{10}}{2*-2}=\frac{4-2\sqrt{10}}{-4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{10}}{2*-2}=\frac{4+2\sqrt{10}}{-4}
$