x^2-6x+9/4=0

Solution for x^2-6x+9/4=0 equation:

x^2-6x+9/4=0

We multiply all the terms by the denominator


x^2*4-6x*4+9=0

Wy multiply elements

4x^2-24x+9=0

a = 4; b = -24; c = +9;
Δ = b2-4ac
Δ = -242-4·4·9
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12\sqrt{3}}{2*4}=\frac{24-12\sqrt{3}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12\sqrt{3}}{2*4}=\frac{24+12\sqrt{3}}{8}
$