X2-12x=265

Solution for X2-12x=265 equation:

X2-12X=265

We move all terms to the left:

X2-12X-(265)=0

We add all the numbers together, and all the variables

X^2-12X-265=0

a = 1; b = -12; c = -265;
Δ = b2-4ac
Δ = -122-4·1·(-265)
Δ = 1204
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:

$\sqrt{\Delta}=\sqrt{1204}=\sqrt{4*301}=\sqrt{4}*\sqrt{301}=2\sqrt{301}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{301}}{2*1}=\frac{12-2\sqrt{301}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{301}}{2*1}=\frac{12+2\sqrt{301}}{2}
$