X^2+2x=5/4

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

X^2+2X=5/4

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

4X^2+8X-5=0

a = 4; b = 8; c = -5;
Δ = b2-4ac
Δ = 82-4·4·(-5)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-12}{2*4}=\frac{-20}{8}
=-2+1/2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+12}{2*4}=\frac{4}{8}
=1/2
$