x2+3x=-5/4

Solution for x2+3x=-5/4 equation:

x2+3x=-5/4

We move all terms to the left:

x2+3x-(-5/4)=0

We add all the numbers together, and all the variables

x^2+3x-(-5/4)=0

We get rid of parentheses

x^2+3x+5/4=0

We multiply all the terms by the denominator


x^2*4+3x*4+5=0

Wy multiply elements

4x^2+12x+5=0

a = 4; b = 12; c = +5;
Δ = b2-4ac
Δ = 122-4·4·5
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-8}{2*4}=\frac{-20}{8}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+8}{2*4}=\frac{-4}{8}
=-1/2
$