3x(8x+15x)=180

Solution for 3x(8x+15x)=180 equation:

3x(8x+15x)=180

We move all terms to the left:

3x(8x+15x)-(180)=0

We add all the numbers together, and all the variables

3x(+23x)-180=0

We multiply parentheses

69x^2-180=0

a = 69; b = 0; c = -180;
Δ = b2-4ac
Δ = 02-4·69·(-180)
Δ = 49680
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:

$\sqrt{\Delta}=\sqrt{49680}=\sqrt{144*345}=\sqrt{144}*\sqrt{345}=12\sqrt{345}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{345}}{2*69}=\frac{0-12\sqrt{345}}{138}
=-\frac{12\sqrt{345}}{138}
=-\frac{2\sqrt{345}}{23}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{345}}{2*69}=\frac{0+12\sqrt{345}}{138}
=\frac{12\sqrt{345}}{138}
=\frac{2\sqrt{345}}{23}
$