Y=x^2+5x-17.

Solution for Y=x^2+5x-17. equation:

=Y^2+5Y-17.

We move all terms to the left:

-(Y^2+5Y-17.)=0

We get rid of parentheses

-Y^2-5Y+17.=0

We add all the numbers together, and all the variables

-1Y^2-5Y+17=0

a = -1; b = -5; c = +17;
Δ = b2-4ac
Δ = -52-4·(-1)·17
Δ = 93
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{93}}{2*-1}=\frac{5-\sqrt{93}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{93}}{2*-1}=\frac{5+\sqrt{93}}{-2}
$