16x^2+96x+11=59

Solution for 16x^2+96x+11=59 equation:

16x^2+96x+11=59

We move all terms to the left:

16x^2+96x+11-(59)=0

We add all the numbers together, and all the variables

16x^2+96x-48=0

a = 16; b = 96; c = -48;
Δ = b2-4ac
Δ = 962-4·16·(-48)
Δ = 12288
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:

$\sqrt{\Delta}=\sqrt{12288}=\sqrt{4096*3}=\sqrt{4096}*\sqrt{3}=64\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-64\sqrt{3}}{2*16}=\frac{-96-64\sqrt{3}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+64\sqrt{3}}{2*16}=\frac{-96+64\sqrt{3}}{32}
$