-5(x/15-16)-30=50-1/3x

Solution for -5(x/15-16)-30=50-1/3x equation:

-5(x/15-16)-30=50-1/3x

We move all terms to the left:

-5(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

-5(x/15-16)-(-1/3x+50)-30=0

We multiply parentheses

-5x-(-1/3x+50)+80-30=0

We get rid of parentheses

-5x+1/3x-50+80-30=0

We multiply all the terms by the denominator


-5x*3x-50*3x+80*3x-30*3x+1=0

Wy multiply elements

-15x^2-150x+240x-90x+1=0

We add all the numbers together, and all the variables

-15x^2+1=0

a = -15; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-15)·1
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{15}}{2*-15}=\frac{0-2\sqrt{15}}{-30}
=-\frac{2\sqrt{15}}{-30}
=-\frac{\sqrt{15}}{-15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{15}}{2*-15}=\frac{0+2\sqrt{15}}{-30}
=\frac{2\sqrt{15}}{-30}
=\frac{\sqrt{15}}{-15}
$