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

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

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

We move all terms to the left:

-5((x)/(15)-16-30)-(50-(1)/(3)x)=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/15-46)-(-1/3x+50)=0

We multiply parentheses

-5x-(-1/3x+50)+230=0

We get rid of parentheses

-5x+1/3x-50+230=0

We multiply all the terms by the denominator


-5x*3x-50*3x+230*3x+1=0

Wy multiply elements

-15x^2-150x+690x+1=0

We add all the numbers together, and all the variables

-15x^2+540x+1=0

a = -15; b = 540; c = +1;
Δ = b2-4ac
Δ = 5402-4·(-15)·1
Δ = 291660
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:

$\sqrt{\Delta}=\sqrt{291660}=\sqrt{4*72915}=\sqrt{4}*\sqrt{72915}=2\sqrt{72915}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(540)-2\sqrt{72915}}{2*-15}=\frac{-540-2\sqrt{72915}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(540)+2\sqrt{72915}}{2*-15}=\frac{-540+2\sqrt{72915}}{-30}
$