x^2-4x-74=3

Solution for x^2-4x-74=3 equation:

x^2-4x-74=3

We move all terms to the left:

x^2-4x-74-(3)=0

We add all the numbers together, and all the variables

x^2-4x-77=0

a = 1; b = -4; c = -77;
Δ = b2-4ac
Δ = -42-4·1·(-77)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-18}{2*1}=\frac{-14}{2}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+18}{2*1}=\frac{22}{2}
=11
$