1+3x+9x^2=10

Solution for 1+3x+9x^2=10 equation:

1+3x+9x^2=10

We move all terms to the left:

1+3x+9x^2-(10)=0

We add all the numbers together, and all the variables

9x^2+3x-9=0

a = 9; b = 3; c = -9;
Δ = b2-4ac
Δ = 32-4·9·(-9)
Δ = 333
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:

$\sqrt{\Delta}=\sqrt{333}=\sqrt{9*37}=\sqrt{9}*\sqrt{37}=3\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{37}}{2*9}=\frac{-3-3\sqrt{37}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{37}}{2*9}=\frac{-3+3\sqrt{37}}{18}
$