9-1/2x=5x-1

Solution for 9-1/2x=5x-1 equation:

9-1/2x=5x-1

We move all terms to the left:

9-1/2x-(5x-1)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

-1/2x-5x+1+9=0

We multiply all the terms by the denominator


-5x*2x+1*2x+9*2x-1=0

Wy multiply elements

-10x^2+2x+18x-1=0

We add all the numbers together, and all the variables

-10x^2+20x-1=0

a = -10; b = 20; c = -1;
Δ = b2-4ac
Δ = 202-4·(-10)·(-1)
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-6\sqrt{10}}{2*-10}=\frac{-20-6\sqrt{10}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+6\sqrt{10}}{2*-10}=\frac{-20+6\sqrt{10}}{-20}
$