X^2-9x+(81/4)=(1/4)

Solution for X^2-9x+(81/4)=(1/4) equation:

X^2-9X+(81/4)=(1/4)

We move all terms to the left:

X^2-9X+(81/4)-((1/4))=0

We add all the numbers together, and all the variables

X^2-9X+(+81/4)-((+1/4))=0

We get rid of parentheses

X^2-9X+81/4-((+1/4))=0

We calculate fractions


X^2-9X=0

a = 1; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·1·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*1}=\frac{0}{2}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*1}=\frac{18}{2}
=9
$