3x(4x+5x)=81

Solution for 3x(4x+5x)=81 equation:

3x(4x+5x)=81

We move all terms to the left:

3x(4x+5x)-(81)=0

We add all the numbers together, and all the variables

3x(+9x)-81=0

We multiply parentheses

27x^2-81=0

a = 27; b = 0; c = -81;
Δ = b2-4ac
Δ = 02-4·27·(-81)
Δ = 8748
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:

$\sqrt{\Delta}=\sqrt{8748}=\sqrt{2916*3}=\sqrt{2916}*\sqrt{3}=54\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-54\sqrt{3}}{2*27}=\frac{0-54\sqrt{3}}{54}
=-\frac{54\sqrt{3}}{54}
=-\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+54\sqrt{3}}{2*27}=\frac{0+54\sqrt{3}}{54}
=\frac{54\sqrt{3}}{54}
=\sqrt{3}
$