2(x^2+5x)=1/64

Solution for 2(x^2+5x)=1/64 equation:

2(x^2+5x)=1/64

We move all terms to the left:

2(x^2+5x)-(1/64)=0

We add all the numbers together, and all the variables

2(x^2+5x)-(+1/64)=0

We multiply parentheses

2x^2+10x-(+1/64)=0

We get rid of parentheses

2x^2+10x-1/64=0

We multiply all the terms by the denominator


2x^2*64+10x*64-1=0

Wy multiply elements

128x^2+640x-1=0

a = 128; b = 640; c = -1;
Δ = b2-4ac
Δ = 6402-4·128·(-1)
Δ = 410112
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:

$\sqrt{\Delta}=\sqrt{410112}=\sqrt{2304*178}=\sqrt{2304}*\sqrt{178}=48\sqrt{178}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(640)-48\sqrt{178}}{2*128}=\frac{-640-48\sqrt{178}}{256}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(640)+48\sqrt{178}}{2*128}=\frac{-640+48\sqrt{178}}{256}
$