x^2+7x+49/4=4

Solution for x^2+7x+49/4=4 equation:

x^2+7x+49/4=4

We move all terms to the left:

x^2+7x+49/4-(4)=0

determiningTheFunctionDomain
x^2+7x-4+49/4=0

We multiply all the terms by the denominator


x^2*4+7x*4+49-4*4=0

We add all the numbers together, and all the variables

x^2*4+7x*4+33=0

Wy multiply elements

4x^2+28x+33=0

a = 4; b = 28; c = +33;
Δ = b2-4ac
Δ = 282-4·4·33
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-16}{2*4}=\frac{-44}{8}
=-5+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+16}{2*4}=\frac{-12}{8}
=-1+1/2
$