Y=3-8x-x2

Solution for Y=3-8x-x2 equation:

=3-8Y-Y2

We move all terms to the left:

-(3-8Y-Y2)=0

We add all the numbers together, and all the variables

-(-8Y-1Y^2+3)=0

We get rid of parentheses

1Y^2+8Y-3=0

We add all the numbers together, and all the variables

Y^2+8Y-3=0

a = 1; b = 8; c = -3;
Δ = b2-4ac
Δ = 82-4·1·(-3)
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{19}}{2*1}=\frac{-8-2\sqrt{19}}{2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{19}}{2*1}=\frac{-8+2\sqrt{19}}{2}
$