7(x+1)=x^2-23

Solution for 7(x+1)=x^2-23 equation:

7(x+1)=x^2-23

We move all terms to the left:

7(x+1)-(x^2-23)=0

We multiply parentheses

7x-(x^2-23)+7=0

We get rid of parentheses

-x^2+7x+23+7=0

We add all the numbers together, and all the variables

-1x^2+7x+30=0

a = -1; b = 7; c = +30;
Δ = b2-4ac
Δ = 72-4·(-1)·30
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-13}{2*-1}=\frac{-20}{-2}
=+10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+13}{2*-1}=\frac{6}{-2}
=-3
$