Y=x2-8x-7

Solution for Y=x2-8x-7 equation:

=Y2-8Y-7

We move all terms to the left:

-(Y2-8Y-7)=0

We add all the numbers together, and all the variables

-(+Y^2-8Y-7)=0

We get rid of parentheses

-Y^2+8Y+7=0

We add all the numbers together, and all the variables

-1Y^2+8Y+7=0

a = -1; b = 8; c = +7;
Δ = b2-4ac
Δ = 82-4·(-1)·7
Δ = 92
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:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{23}}{2*-1}=\frac{-8-2\sqrt{23}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{23}}{2*-1}=\frac{-8+2\sqrt{23}}{-2}
$