23(x)=x^2+7

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

23(x)=x^2+7

We move all terms to the left:

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

We get rid of parentheses

-x^2+23x-7=0

We add all the numbers together, and all the variables

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

a = -1; b = 23; c = -7;
Δ = b2-4ac
Δ = 232-4·(-1)·(-7)
Δ = 501
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-\sqrt{501}}{2*-1}=\frac{-23-\sqrt{501}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+\sqrt{501}}{2*-1}=\frac{-23+\sqrt{501}}{-2}
$