Y=x^2+6x-71

Solution for Y=x^2+6x-71 equation:

=Y^2+6Y-71

We move all terms to the left:

-(Y^2+6Y-71)=0

We get rid of parentheses

-Y^2-6Y+71=0

We add all the numbers together, and all the variables

-1Y^2-6Y+71=0

a = -1; b = -6; c = +71;
Δ = b2-4ac
Δ = -62-4·(-1)·71
Δ = 320
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:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-8\sqrt{5}}{2*-1}=\frac{6-8\sqrt{5}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+8\sqrt{5}}{2*-1}=\frac{6+8\sqrt{5}}{-2}
$