X2-3x-13.75=0

Solution for X2-3x-13.75=0 equation:

X2-3X-13.75=0

We add all the numbers together, and all the variables

X^2-3X-13.75=0

a = 1; b = -3; c = -13.75;
Δ = b2-4ac
Δ = -32-4·1·(-13.75)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-8}{2*1}=\frac{-5}{2}
=-2+1/2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+8}{2*1}=\frac{11}{2}
=5+1/2
$