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

Solution for x^2+9x-81/4=0 equation:

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}
$