X-15(-1/3)(x-15)=32

Solution for X-15(-1/3)(x-15)=32 equation:

X-15(-1/3)(X-15)=32

We move all terms to the left:

X-15(-1/3)(X-15)-(32)=0


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

X∈R


We multiply parentheses ..

-15(-1X^2-1/3*-15)+X-32=0

We multiply all the terms by the denominator


-15(-1X^2-1+X*3*-15)-32*3*-15)=0

We add all the numbers together, and all the variables

-15(-1X^2-1+X*3*-15)=0

We multiply parentheses

15X^2-45X^2+15+225=0

We add all the numbers together, and all the variables

-30X^2+240=0

a = -30; b = 0; c = +240;
Δ = b2-4ac
Δ = 02-4·(-30)·240
Δ = 28800
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:

$\sqrt{\Delta}=\sqrt{28800}=\sqrt{14400*2}=\sqrt{14400}*\sqrt{2}=120\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-120\sqrt{2}}{2*-30}=\frac{0-120\sqrt{2}}{-60}
=-\frac{120\sqrt{2}}{-60}
=-\frac{2\sqrt{2}}{-1}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+120\sqrt{2}}{2*-30}=\frac{0+120\sqrt{2}}{-60}
=\frac{120\sqrt{2}}{-60}
=\frac{2\sqrt{2}}{-1}
$