x^2+6x+6=49/4

Solution for x^2+6x+6=49/4 equation:

x^2+6x+6=49/4

We move all terms to the left:

x^2+6x+6-(49/4)=0

We add all the numbers together, and all the variables

x^2+6x+6-(+49/4)=0

We get rid of parentheses

x^2+6x+6-49/4=0

We multiply all the terms by the denominator


x^2*4+6x*4-49+6*4=0

We add all the numbers together, and all the variables

x^2*4+6x*4-25=0

Wy multiply elements

4x^2+24x-25=0

a = 4; b = 24; c = -25;
Δ = b2-4ac
Δ = 242-4·4·(-25)
Δ = 976
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:

$\sqrt{\Delta}=\sqrt{976}=\sqrt{16*61}=\sqrt{16}*\sqrt{61}=4\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{61}}{2*4}=\frac{-24-4\sqrt{61}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{61}}{2*4}=\frac{-24+4\sqrt{61}}{8}
$