x+9x2-9=1-x=3

Solution for x+9x2-9=1-x=3 equation:

x+9x^2-9=1-x=3

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

9x^2+x+1x-1-9=0

We add all the numbers together, and all the variables

9x^2+2x-10=0

a = 9; b = 2; c = -10;
Δ = b2-4ac
Δ = 22-4·9·(-10)
Δ = 364
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:

$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{91}}{2*9}=\frac{-2-2\sqrt{91}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{91}}{2*9}=\frac{-2+2\sqrt{91}}{18}
$