2(x^2+7x)=8^(-4)

Solution for 2(x^2+7x)=8^(-4) equation:

2(x^2+7x)=8^(-4)

We move all terms to the left:

2(x^2+7x)-(8^(-4))=0

We add all the numbers together, and all the variables

2(x^2+7x)-0.000244140625=0

We multiply parentheses

2x^2+14x-0.000244140625=0

a = 2; b = 14; c = -0.000244140625;
Δ = b2-4ac
Δ = 142-4·2·(-0.000244140625)
Δ = 196.001953125
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-\sqrt{196.001953125}}{2*2}=\frac{-14-\sqrt{196.001953125}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+\sqrt{196.001953125}}{2*2}=\frac{-14+\sqrt{196.001953125}}{4}
$