-2x(1+4x)5=-13

Solution for -2x(1+4x)5=-13 equation:

-2x(1+4x)5=-13

We move all terms to the left:

-2x(1+4x)5-(-13)=0

We add all the numbers together, and all the variables

-2x(4x+1)5-(-13)=0

We add all the numbers together, and all the variables

-2x(4x+1)5+13=0

We multiply parentheses

-40x^2-10x+13=0

a = -40; b = -10; c = +13;
Δ = b2-4ac
Δ = -102-4·(-40)·13
Δ = 2180
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:

$\sqrt{\Delta}=\sqrt{2180}=\sqrt{4*545}=\sqrt{4}*\sqrt{545}=2\sqrt{545}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{545}}{2*-40}=\frac{10-2\sqrt{545}}{-80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{545}}{2*-40}=\frac{10+2\sqrt{545}}{-80}
$