x^2-4x-76=3

Solution for x^2-4x-76=3 equation:

x^2-4x-76=3

We move all terms to the left:

x^2-4x-76-(3)=0

We add all the numbers together, and all the variables

x^2-4x-79=0

a = 1; b = -4; c = -79;
Δ = b2-4ac
Δ = -42-4·1·(-79)
Δ = 332
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:

$\sqrt{\Delta}=\sqrt{332}=\sqrt{4*83}=\sqrt{4}*\sqrt{83}=2\sqrt{83}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{83}}{2*1}=\frac{4-2\sqrt{83}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{83}}{2*1}=\frac{4+2\sqrt{83}}{2}
$