x(x+8)-7=23

Solution for x(x+8)-7=23 equation:

x(x+8)-7=23

We move all terms to the left:

x(x+8)-7-(23)=0

We add all the numbers together, and all the variables

x(x+8)-30=0

We multiply parentheses

x^2+8x-30=0

a = 1; b = 8; c = -30;
Δ = b2-4ac
Δ = 82-4·1·(-30)
Δ = 184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{46}}{2*1}=\frac{-8-2\sqrt{46}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{46}}{2*1}=\frac{-8+2\sqrt{46}}{2}
$