-5x+200=-31/3x+150

Solution for -5x+200=-31/3x+150 equation:

-5x+200=-31/3x+150

We move all terms to the left:

-5x+200-(-31/3x+150)=0


Domain of the equation: 3x+150)!=0

x∈R


We get rid of parentheses

-5x+31/3x-150+200=0

We multiply all the terms by the denominator


-5x*3x-150*3x+200*3x+31=0

Wy multiply elements

-15x^2-450x+600x+31=0

We add all the numbers together, and all the variables

-15x^2+150x+31=0

a = -15; b = 150; c = +31;
Δ = b2-4ac
Δ = 1502-4·(-15)·31
Δ = 24360
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:

$\sqrt{\Delta}=\sqrt{24360}=\sqrt{4*6090}=\sqrt{4}*\sqrt{6090}=2\sqrt{6090}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(150)-2\sqrt{6090}}{2*-15}=\frac{-150-2\sqrt{6090}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(150)+2\sqrt{6090}}{2*-15}=\frac{-150+2\sqrt{6090}}{-30}
$