X^2-5x=9/4

Solution for X^2-5x=9/4 equation:

X^2-5X=9/4

We move all terms to the left:

X^2-5X-(9/4)=0

We add all the numbers together, and all the variables

X^2-5X-(+9/4)=0

We get rid of parentheses

X^2-5X-9/4=0

We multiply all the terms by the denominator


X^2*4-5X*4-9=0

Wy multiply elements

4X^2-20X-9=0

a = 4; b = -20; c = -9;
Δ = b2-4ac
Δ = -202-4·4·(-9)
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{34}}{2*4}=\frac{20-4\sqrt{34}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{34}}{2*4}=\frac{20+4\sqrt{34}}{8}
$