4x2+4x+1=49

Solution for 4x2+4x+1=49 equation:

4x^2+4x+1=49

We move all terms to the left:

4x^2+4x+1-(49)=0

We add all the numbers together, and all the variables

4x^2+4x-48=0

a = 4; b = 4; c = -48;
Δ = b2-4ac
Δ = 42-4·4·(-48)
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{-(4)-28}{2*4}=\frac{-32}{8}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+28}{2*4}=\frac{24}{8}
=3
$