x^2+x=5/4

Solution for x^2+x=5/4 equation:

x^2+x=5/4

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

x^2+x-5/4=0

We multiply all the terms by the denominator


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

Wy multiply elements

4x^2+4x-5=0

a = 4; b = 4; c = -5;
Δ = b2-4ac
Δ = 42-4·4·(-5)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{6}}{2*4}=\frac{-4-4\sqrt{6}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{6}}{2*4}=\frac{-4+4\sqrt{6}}{8}
$