x^2-3x-4=4.75

Solution for x^2-3x-4=4.75 equation:

x^2-3x-4=4.75

We move all terms to the left:

x^2-3x-4-(4.75)=0

We add all the numbers together, and all the variables

x^2-3x-8.75=0

a = 1; b = -3; c = -8.75;
Δ = b2-4ac
Δ = -32-4·1·(-8.75)
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-2\sqrt{11}}{2*1}=\frac{3-2\sqrt{11}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+2\sqrt{11}}{2*1}=\frac{3+2\sqrt{11}}{2}
$