(x+6)3x=90

Solution for (x+6)3x=90 equation:

(x+6)3x=90

We move all terms to the left:

(x+6)3x-(90)=0

We multiply parentheses

3x^2+18x-90=0

a = 3; b = 18; c = -90;
Δ = b2-4ac
Δ = 182-4·3·(-90)
Δ = 1404
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:

$\sqrt{\Delta}=\sqrt{1404}=\sqrt{36*39}=\sqrt{36}*\sqrt{39}=6\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{39}}{2*3}=\frac{-18-6\sqrt{39}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{39}}{2*3}=\frac{-18+6\sqrt{39}}{6}
$