3x(9^x+1)=60

Solution for 3x(9^x+1)=60 equation:

3x(9^x+1)=60

We move all terms to the left:

3x(9^x+1)-(60)=0

We multiply parentheses

27x^2+3x-60=0

a = 27; b = 3; c = -60;
Δ = b2-4ac
Δ = 32-4·27·(-60)
Δ = 6489
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:

$\sqrt{\Delta}=\sqrt{6489}=\sqrt{9*721}=\sqrt{9}*\sqrt{721}=3\sqrt{721}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{721}}{2*27}=\frac{-3-3\sqrt{721}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{721}}{2*27}=\frac{-3+3\sqrt{721}}{54}
$