X^2-12x-43=65

Solution for X^2-12x-43=65 equation:

X^2-12X-43=65

We move all terms to the left:

X^2-12X-43-(65)=0

We add all the numbers together, and all the variables

X^2-12X-108=0

a = 1; b = -12; c = -108;
Δ = b2-4ac
Δ = -122-4·1·(-108)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-24}{2*1}=\frac{-12}{2}
=-6
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+24}{2*1}=\frac{36}{2}
=18
$