x^2-4x-2=43

Solution for x^2-4x-2=43 equation:

x^2-4x-2=43

We move all terms to the left:

x^2-4x-2-(43)=0

We add all the numbers together, and all the variables

x^2-4x-45=0

a = 1; b = -4; c = -45;
Δ = b2-4ac
Δ = -42-4·1·(-45)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-14}{2*1}=\frac{-10}{2}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+14}{2*1}=\frac{18}{2}
=9
$