x^2-9x+5/4=0

Solution for x^2-9x+5/4=0 equation:

x^2-9x+5/4=0

We multiply all the terms by the denominator


x^2*4-9x*4+5=0

Wy multiply elements

4x^2-36x+5=0

a = 4; b = -36; c = +5;
Δ = b2-4ac
Δ = -362-4·4·5
Δ = 1216
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:

$\sqrt{\Delta}=\sqrt{1216}=\sqrt{64*19}=\sqrt{64}*\sqrt{19}=8\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-8\sqrt{19}}{2*4}=\frac{36-8\sqrt{19}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+8\sqrt{19}}{2*4}=\frac{36+8\sqrt{19}}{8}
$