X^2-12x+24=3

Solution for X^2-12x+24=3 equation:

X^2-12X+24=3

We move all terms to the left:

X^2-12X+24-(3)=0

We add all the numbers together, and all the variables

X^2-12X+21=0

a = 1; b = -12; c = +21;
Δ = b2-4ac
Δ = -122-4·1·21
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{15}}{2*1}=\frac{12-2\sqrt{15}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{15}}{2*1}=\frac{12+2\sqrt{15}}{2}
$