X^2-24x+113.75=0

Solution for X^2-24x+113.75=0 equation:

X^2-24X+113.75=0

a = 1; b = -24; c = +113.75;
Δ = b2-4ac
Δ = -242-4·1·113.75
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-11}{2*1}=\frac{13}{2}
=6+1/2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+11}{2*1}=\frac{35}{2}
=17+1/2
$