X2+12x-261=0

Solution for X2+12x-261=0 equation:

X2+12X-261=0

We add all the numbers together, and all the variables

X^2+12X-261=0

a = 1; b = 12; c = -261;
Δ = b2-4ac
Δ = 122-4·1·(-261)
Δ = 1188
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:

$\sqrt{\Delta}=\sqrt{1188}=\sqrt{36*33}=\sqrt{36}*\sqrt{33}=6\sqrt{33}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{33}}{2*1}=\frac{-12-6\sqrt{33}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{33}}{2*1}=\frac{-12+6\sqrt{33}}{2}
$