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X^2-9X+81/4=129/4
We move all terms to the left:
X^2-9X+81/4-(129/4)=0
We add all the numbers together, and all the variables
X^2-9X+81/4-(+129/4)=0
We get rid of parentheses
X^2-9X+81/4-129/4=0
We multiply all the terms by the denominator
X^2*4-9X*4+81-129=0
We add all the numbers together, and all the variables
X^2*4-9X*4-48=0
Wy multiply elements
4X^2-36X-48=0
a = 4; b = -36; c = -48;
Δ = b2-4ac
Δ = -362-4·4·(-48)
Δ = 2064
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2064}=\sqrt{16*129}=\sqrt{16}*\sqrt{129}=4\sqrt{129}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{129}}{2*4}=\frac{36-4\sqrt{129}}{8} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{129}}{2*4}=\frac{36+4\sqrt{129}}{8} $
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