X=-2y^2-8y+3

Solution for X=-2y^2-8y+3 equation:

X=-2X^2-8X+3

We move all terms to the left:

X-(-2X^2-8X+3)=0

We get rid of parentheses

2X^2+8X+X-3=0

We add all the numbers together, and all the variables

2X^2+9X-3=0

a = 2; b = 9; c = -3;
Δ = b2-4ac
Δ = 92-4·2·(-3)
Δ = 105
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{105}}{2*2}=\frac{-9-\sqrt{105}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{105}}{2*2}=\frac{-9+\sqrt{105}}{4}
$