Y=x^2+16x-7

Solution for Y=x^2+16x-7 equation:

=Y^2+16Y-7

We move all terms to the left:

-(Y^2+16Y-7)=0

We get rid of parentheses

-Y^2-16Y+7=0

We add all the numbers together, and all the variables

-1Y^2-16Y+7=0

a = -1; b = -16; c = +7;
Δ = b2-4ac
Δ = -162-4·(-1)·7
Δ = 284
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:

$\sqrt{\Delta}=\sqrt{284}=\sqrt{4*71}=\sqrt{4}*\sqrt{71}=2\sqrt{71}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{71}}{2*-1}=\frac{16-2\sqrt{71}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{71}}{2*-1}=\frac{16+2\sqrt{71}}{-2}
$