123-x^2=10(x)

Solution for 123-x^2=10(x) equation:

123-x^2=10(x)

We move all terms to the left:

123-x^2-(10(x))=0

determiningTheFunctionDomain
-x^2-10x+123=0

We add all the numbers together, and all the variables

-1x^2-10x+123=0

a = -1; b = -10; c = +123;
Δ = b2-4ac
Δ = -102-4·(-1)·123
Δ = 592
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:

$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-4\sqrt{37}}{2*-1}=\frac{10-4\sqrt{37}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+4\sqrt{37}}{2*-1}=\frac{10+4\sqrt{37}}{-2}
$