2x(x+4)+5=61

Solution for 2x(x+4)+5=61 equation:

2x(x+4)+5=61

We move all terms to the left:

2x(x+4)+5-(61)=0

We add all the numbers together, and all the variables

2x(x+4)-56=0

We multiply parentheses

2x^2+8x-56=0

a = 2; b = 8; c = -56;
Δ = b2-4ac
Δ = 82-4·2·(-56)
Δ = 512
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:

$\sqrt{\Delta}=\sqrt{512}=\sqrt{256*2}=\sqrt{256}*\sqrt{2}=16\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-16\sqrt{2}}{2*2}=\frac{-8-16\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+16\sqrt{2}}{2*2}=\frac{-8+16\sqrt{2}}{4}
$