8x^2-51x+55.25=0

Solution for 8x^2-51x+55.25=0 equation:

8x^2-51x+55.25=0

a = 8; b = -51; c = +55.25;
Δ = b2-4ac
Δ = -512-4·8·55.25
Δ = 833
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:

$\sqrt{\Delta}=\sqrt{833}=\sqrt{49*17}=\sqrt{49}*\sqrt{17}=7\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-7\sqrt{17}}{2*8}=\frac{51-7\sqrt{17}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+7\sqrt{17}}{2*8}=\frac{51+7\sqrt{17}}{16}
$