x^2-3x-9/4=0

Solution for x^2-3x-9/4=0 equation:

x^2-3x-9/4=0

We multiply all the terms by the denominator


x^2*4-3x*4-9=0

Wy multiply elements

4x^2-12x-9=0

a = 4; b = -12; c = -9;
Δ = b2-4ac
Δ = -122-4·4·(-9)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{2}}{2*4}=\frac{12-12\sqrt{2}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{2}}{2*4}=\frac{12+12\sqrt{2}}{8}
$