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x^2-9x+29/4=0
We multiply all the terms by the denominator
x^2*4-9x*4+29=0
Wy multiply elements
4x^2-36x+29=0
a = 4; b = -36; c = +29;
Δ = b2-4ac
Δ = -362-4·4·29
Δ = 832
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{832}=\sqrt{64*13}=\sqrt{64}*\sqrt{13}=8\sqrt{13}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-8\sqrt{13}}{2*4}=\frac{36-8\sqrt{13}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+8\sqrt{13}}{2*4}=\frac{36+8\sqrt{13}}{8} $
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