x2+6x+9=49/4

Solution for x2+6x+9=49/4 equation:

x2+6x+9=49/4

We move all terms to the left:

x2+6x+9-(49/4)=0

We add all the numbers together, and all the variables

x2+6x+9-(+49/4)=0

We add all the numbers together, and all the variables

x^2+6x+9-(+49/4)=0

We get rid of parentheses

x^2+6x+9-49/4=0

We multiply all the terms by the denominator


x^2*4+6x*4-49+9*4=0

We add all the numbers together, and all the variables

x^2*4+6x*4-13=0

Wy multiply elements

4x^2+24x-13=0

a = 4; b = 24; c = -13;
Δ = b2-4ac
Δ = 242-4·4·(-13)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-28}{2*4}=\frac{-52}{8}
=-6+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+28}{2*4}=\frac{4}{8}
=1/2
$