7x-8x(x+3)=1

Solution for 7x-8x(x+3)=1 equation:

7x-8x(x+3)=1

We move all terms to the left:

7x-8x(x+3)-(1)=0

We multiply parentheses

-8x^2+7x-24x-1=0

We add all the numbers together, and all the variables

-8x^2-17x-1=0

a = -8; b = -17; c = -1;
Δ = b2-4ac
Δ = -172-4·(-8)·(-1)
Δ = 257
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{-(-17)-\sqrt{257}}{2*-8}=\frac{17-\sqrt{257}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{257}}{2*-8}=\frac{17+\sqrt{257}}{-16}
$