6x^2=1-9x

Solution for 6x^2=1-9x equation:

6x^2=1-9x

We move all terms to the left:

6x^2-(1-9x)=0

We add all the numbers together, and all the variables

6x^2-(-9x+1)=0

We get rid of parentheses

6x^2+9x-1=0

a = 6; b = 9; c = -1;
Δ = b2-4ac
Δ = 92-4·6·(-1)
Δ = 105
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{105}}{2*6}=\frac{-9-\sqrt{105}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{105}}{2*6}=\frac{-9+\sqrt{105}}{12}
$