(x-50)3x=150

Solution for (x-50)3x=150 equation:

(x-50)3x=150

We move all terms to the left:

(x-50)3x-(150)=0

We multiply parentheses

3x^2-150x-150=0

a = 3; b = -150; c = -150;
Δ = b2-4ac
Δ = -1502-4·3·(-150)
Δ = 24300
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:

$\sqrt{\Delta}=\sqrt{24300}=\sqrt{8100*3}=\sqrt{8100}*\sqrt{3}=90\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-90\sqrt{3}}{2*3}=\frac{150-90\sqrt{3}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+90\sqrt{3}}{2*3}=\frac{150+90\sqrt{3}}{6}
$