X2-5x=231/4

Solution for X2-5x=231/4 equation:

X2-5X=231/4

We move all terms to the left:

X2-5X-(231/4)=0

We add all the numbers together, and all the variables

X2-5X-(+231/4)=0

We add all the numbers together, and all the variables

X^2-5X-(+231/4)=0

We get rid of parentheses

X^2-5X-231/4=0

We multiply all the terms by the denominator


X^2*4-5X*4-231=0

Wy multiply elements

4X^2-20X-231=0

a = 4; b = -20; c = -231;
Δ = b2-4ac
Δ = -202-4·4·(-231)
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-64}{2*4}=\frac{-44}{8}
=-5+1/2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+64}{2*4}=\frac{84}{8}
=10+1/2
$