1.5x^2=6x+360

Solution for 1.5x^2=6x+360 equation:

1.5x^2=6x+360

We move all terms to the left:

1.5x^2-(6x+360)=0

We get rid of parentheses

1.5x^2-6x-360=0

a = 1.5; b = -6; c = -360;
Δ = b2-4ac
Δ = -62-4·1.5·(-360)
Δ = 2196
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:

$\sqrt{\Delta}=\sqrt{2196}=\sqrt{36*61}=\sqrt{36}*\sqrt{61}=6\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{61}}{2*1.5}=\frac{6-6\sqrt{61}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{61}}{2*1.5}=\frac{6+6\sqrt{61}}{3}
$