8(x-2)3x=61

Solution for 8(x-2)3x=61 equation:

8(x-2)3x=61

We move all terms to the left:

8(x-2)3x-(61)=0

We multiply parentheses

24x^2-48x-61=0

a = 24; b = -48; c = -61;
Δ = b2-4ac
Δ = -482-4·24·(-61)
Δ = 8160
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:

$\sqrt{\Delta}=\sqrt{8160}=\sqrt{16*510}=\sqrt{16}*\sqrt{510}=4\sqrt{510}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{510}}{2*24}=\frac{48-4\sqrt{510}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{510}}{2*24}=\frac{48+4\sqrt{510}}{48}
$