x^2-x-(143/4)=0

Solution for x^2-x-(143/4)=0 equation:

x^2-x-(143/4)=0

We add all the numbers together, and all the variables

x^2-x-(+143/4)=0

We add all the numbers together, and all the variables

x^2-1x-(+143/4)=0

We get rid of parentheses

x^2-1x-143/4=0

We multiply all the terms by the denominator


x^2*4-1x*4-143=0

Wy multiply elements

4x^2-4x-143=0

a = 4; b = -4; c = -143;
Δ = b2-4ac
Δ = -42-4·4·(-143)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-48}{2*4}=\frac{-44}{8}
=-5+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+48}{2*4}=\frac{52}{8}
=6+1/2
$