2*2-6*2+y*y-6*y=7

Solution for 2*2-6*2+y*y-6*y=7 equation:

2*2-6*2+y*y-6y=7

We move all terms to the left:

2*2-6*2+y*y-6y-(7)=0

determiningTheFunctionDomain
y*y-6y-7+2*2-6*2=0

We add all the numbers together, and all the variables

-6y+y*y-15=0

Wy multiply elements

y^2-6y-15=0

a = 1; b = -6; c = -15;
Δ = b2-4ac
Δ = -62-4·1·(-15)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4\sqrt{6}}{2*1}=\frac{6-4\sqrt{6}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4\sqrt{6}}{2*1}=\frac{6+4\sqrt{6}}{2}
$