x^2-9x=81/4

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

x^2-9x=81/4

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

4x^2-36x-81=0

a = 4; b = -36; c = -81;
Δ = b2-4ac
Δ = -362-4·4·(-81)
Δ = 2592
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:

$\sqrt{\Delta}=\sqrt{2592}=\sqrt{1296*2}=\sqrt{1296}*\sqrt{2}=36\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-36\sqrt{2}}{2*4}=\frac{36-36\sqrt{2}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+36\sqrt{2}}{2*4}=\frac{36+36\sqrt{2}}{8}
$