4x^2+8x+4=11

Solution for 4x^2+8x+4=11 equation:

4x^2+8x+4=11

We move all terms to the left:

4x^2+8x+4-(11)=0

We add all the numbers together, and all the variables

4x^2+8x-7=0

a = 4; b = 8; c = -7;
Δ = b2-4ac
Δ = 82-4·4·(-7)
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{11}}{2*4}=\frac{-8-4\sqrt{11}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{11}}{2*4}=\frac{-8+4\sqrt{11}}{8}
$