x^2+6x=-11/4

Solution for x^2+6x=-11/4 equation:

x^2+6x=-11/4

We move all terms to the left:

x^2+6x-(-11/4)=0

We get rid of parentheses

x^2+6x+11/4=0

We multiply all the terms by the denominator


x^2*4+6x*4+11=0

Wy multiply elements

4x^2+24x+11=0

a = 4; b = 24; c = +11;
Δ = b2-4ac
Δ = 242-4·4·11
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-20}{2*4}=\frac{-44}{8}
=-5+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+20}{2*4}=\frac{-4}{8}
=-1/2
$