4(x+5)2x+1=39

Solution for 4(x+5)2x+1=39 equation:

4(x+5)2x+1=39

We move all terms to the left:

4(x+5)2x+1-(39)=0

We add all the numbers together, and all the variables

4(x+5)2x-38=0

We multiply parentheses

8x^2+40x-38=0

a = 8; b = 40; c = -38;
Δ = b2-4ac
Δ = 402-4·8·(-38)
Δ = 2816
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:

$\sqrt{\Delta}=\sqrt{2816}=\sqrt{256*11}=\sqrt{256}*\sqrt{11}=16\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-16\sqrt{11}}{2*8}=\frac{-40-16\sqrt{11}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+16\sqrt{11}}{2*8}=\frac{-40+16\sqrt{11}}{16}
$