8x(3x+7)=8

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

8x(3x+7)=8

We move all terms to the left:

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

We multiply parentheses

24x^2+56x-8=0

a = 24; b = 56; c = -8;
Δ = b2-4ac
Δ = 562-4·24·(-8)
Δ = 3904
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:

$\sqrt{\Delta}=\sqrt{3904}=\sqrt{64*61}=\sqrt{64}*\sqrt{61}=8\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-8\sqrt{61}}{2*24}=\frac{-56-8\sqrt{61}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+8\sqrt{61}}{2*24}=\frac{-56+8\sqrt{61}}{48}
$