(191/2+15)x=150+15x

Solution for (191/2+15)x=150+15x equation:

(191/2+15)x=150+15x

We move all terms to the left:

(191/2+15)x-(150+15x)=0


Domain of the equation: 2+15)x!=0

We move all terms containing x to the left, all other terms to the right

15)x!=-2

x!=-2/1

x!=-2

x∈R


We add all the numbers together, and all the variables

(191/2+15)x-(15x+150)=0

We multiply parentheses

191x^2+15x-(15x+150)=0

We get rid of parentheses

191x^2+15x-15x-150=0

We add all the numbers together, and all the variables

191x^2-150=0

a = 191; b = 0; c = -150;
Δ = b2-4ac
Δ = 02-4·191·(-150)
Δ = 114600
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:

$\sqrt{\Delta}=\sqrt{114600}=\sqrt{100*1146}=\sqrt{100}*\sqrt{1146}=10\sqrt{1146}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{1146}}{2*191}=\frac{0-10\sqrt{1146}}{382}
=-\frac{10\sqrt{1146}}{382}
=-\frac{5\sqrt{1146}}{191}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{1146}}{2*191}=\frac{0+10\sqrt{1146}}{382}
=\frac{10\sqrt{1146}}{382}
=\frac{5\sqrt{1146}}{191}
$