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 multiply all the terms by the denominator


X^2*4-9X*4+81-1=0

We add all the numbers together, and all the variables

X^2*4-9X*4+80=0

Wy multiply elements

4X^2-36X+80=0

a = 4; b = -36; c = +80;
Δ = b2-4ac
Δ = -362-4·4·80
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4}{2*4}=\frac{32}{8}
=4
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4}{2*4}=\frac{40}{8}
=5
$