X(2/3x-15)=180

Solution for X(2/3x-15)=180 equation:

X(2/3X-15)=180

We move all terms to the left:

X(2/3X-15)-(180)=0


Domain of the equation: 3X-15)!=0

X∈R


We multiply parentheses

2X^2-15X-180=0

a = 2; b = -15; c = -180;
Δ = b2-4ac
Δ = -152-4·2·(-180)
Δ = 1665
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:

$\sqrt{\Delta}=\sqrt{1665}=\sqrt{9*185}=\sqrt{9}*\sqrt{185}=3\sqrt{185}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{185}}{2*2}=\frac{15-3\sqrt{185}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{185}}{2*2}=\frac{15+3\sqrt{185}}{4}
$