Y=x^2+7x-16

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

=Y^2+7Y-16

We move all terms to the left:

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

We get rid of parentheses

-Y^2-7Y+16=0

We add all the numbers together, and all the variables

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

a = -1; b = -7; c = +16;
Δ = b2-4ac
Δ = -72-4·(-1)·16
Δ = 113
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{-(-7)-\sqrt{113}}{2*-1}=\frac{7-\sqrt{113}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{113}}{2*-1}=\frac{7+\sqrt{113}}{-2}
$