x^2-9x+81/4=113/4

Solution for x^2-9x+81/4=113/4 equation:

x^2-9x+81/4=113/4

We move all terms to the left:

x^2-9x+81/4-(113/4)=0

We add all the numbers together, and all the variables

x^2-9x+81/4-(+113/4)=0

We get rid of parentheses

x^2-9x+81/4-113/4=0

We multiply all the terms by the denominator


x^2*4-9x*4+81-113=0

We add all the numbers together, and all the variables

x^2*4-9x*4-32=0

Wy multiply elements

4x^2-36x-32=0

a = 4; b = -36; c = -32;
Δ = b2-4ac
Δ = -362-4·4·(-32)
Δ = 1808
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:

$\sqrt{\Delta}=\sqrt{1808}=\sqrt{16*113}=\sqrt{16}*\sqrt{113}=4\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{113}}{2*4}=\frac{36-4\sqrt{113}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{113}}{2*4}=\frac{36+4\sqrt{113}}{8}
$