X2-24x+42=15

Solution for X2-24x+42=15 equation:

X2-24X+42=15

We move all terms to the left:

X2-24X+42-(15)=0

We add all the numbers together, and all the variables

X^2-24X+27=0

a = 1; b = -24; c = +27;
Δ = b2-4ac
Δ = -242-4·1·27
Δ = 468
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:

$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-6\sqrt{13}}{2*1}=\frac{24-6\sqrt{13}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+6\sqrt{13}}{2*1}=\frac{24+6\sqrt{13}}{2}
$