(x-8)3x=180

Solution for (x-8)3x=180 equation:

(x-8)3x=180

We move all terms to the left:

(x-8)3x-(180)=0

We multiply parentheses

3x^2-24x-180=0

a = 3; b = -24; c = -180;
Δ = b2-4ac
Δ = -242-4·3·(-180)
Δ = 2736
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:

$\sqrt{\Delta}=\sqrt{2736}=\sqrt{144*19}=\sqrt{144}*\sqrt{19}=12\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12\sqrt{19}}{2*3}=\frac{24-12\sqrt{19}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12\sqrt{19}}{2*3}=\frac{24+12\sqrt{19}}{6}
$