X^2-x-43=0

Solution for X^2-x-43=0 equation:

X^2-X-43=0

We add all the numbers together, and all the variables

X^2-1X-43=0

a = 1; b = -1; c = -43;
Δ = b2-4ac
Δ = -12-4·1·(-43)
Δ = 173
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{173}}{2*1}=\frac{1-\sqrt{173}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{173}}{2*1}=\frac{1+\sqrt{173}}{2}
$