a^2-8a+7=23

Solution for a^2-8a+7=23 equation:

a^2-8a+7=23

We move all terms to the left:

a^2-8a+7-(23)=0

We add all the numbers together, and all the variables

a^2-8a-16=0

a = 1; b = -8; c = -16;
Δ = b2-4ac
Δ = -82-4·1·(-16)
Δ = 128
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{2}}{2*1}=\frac{8-8\sqrt{2}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{2}}{2*1}=\frac{8+8\sqrt{2}}{2}
$