-1+9x=2+3(-9x+1/2)

Solution for -1+9x=2+3(-9x+1/2) equation:

-1+9x=2+3(-9x+1/2)

We move all terms to the left:

-1+9x-(2+3(-9x+1/2))=0

We multiply all the terms by the denominator


9x*2))-(2+3(-9x+1-1*2))=0

We add all the numbers together, and all the variables

9x*2))-(2+3(-9x-1))=0

We add all the numbers together, and all the variables

-9x+9x*2))-(2+3(=0

Wy multiply elements

18x^2-9x=0

a = 18; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·18·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*18}=\frac{0}{36}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*18}=\frac{18}{36}
=1/2
$