-15(x/15-16)-30=50-1/3x

Solution for -15(x/15-16)-30=50-1/3x equation:

-15(x/15-16)-30=50-1/3x

We move all terms to the left:

-15(x/15-16)-30-(50-1/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-15(x/15-16)-(-1/3x+50)-30=0

We multiply parentheses

-15x-(-1/3x+50)+240-30=0

We get rid of parentheses

-15x+1/3x-50+240-30=0

We multiply all the terms by the denominator


-15x*3x-50*3x+240*3x-30*3x+1=0

Wy multiply elements

-45x^2-150x+720x-90x+1=0

We add all the numbers together, and all the variables

-45x^2+480x+1=0

a = -45; b = 480; c = +1;
Δ = b2-4ac
Δ = 4802-4·(-45)·1
Δ = 230580
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:

$\sqrt{\Delta}=\sqrt{230580}=\sqrt{36*6405}=\sqrt{36}*\sqrt{6405}=6\sqrt{6405}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(480)-6\sqrt{6405}}{2*-45}=\frac{-480-6\sqrt{6405}}{-90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(480)+6\sqrt{6405}}{2*-45}=\frac{-480+6\sqrt{6405}}{-90}
$