x^2-5x+(13/4)=0

Solution for x^2-5x+(13/4)=0 equation:

x^2-5x+(13/4)=0

We add all the numbers together, and all the variables

x^2-5x+(+13/4)=0

We get rid of parentheses

x^2-5x+13/4=0

We multiply all the terms by the denominator


x^2*4-5x*4+13=0

Wy multiply elements

4x^2-20x+13=0

a = 4; b = -20; c = +13;
Δ = b2-4ac
Δ = -202-4·4·13
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-8\sqrt{3}}{2*4}=\frac{20-8\sqrt{3}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+8\sqrt{3}}{2*4}=\frac{20+8\sqrt{3}}{8}
$