5x-1=10(1/2x-1)+9

Solution for 5x-1=10(1/2x-1)+9 equation:

5x-1=10(1/2x-1)+9

We move all terms to the left:

5x-1-(10(1/2x-1)+9)=0


Domain of the equation: 2x-1)+9)!=0

x∈R


We multiply all the terms by the denominator


5x*2x-1*2x-1)+9)-(10(1-1)+9)=0

We add all the numbers together, and all the variables

5x*2x-1*2x-1)+9)-(100+9)=0

We add all the numbers together, and all the variables

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

Wy multiply elements

10x^2-2x=0

a = 10; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·10·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*10}=\frac{0}{20}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*10}=\frac{4}{20}
=1/5
$