x2+3=9x

Solution for x2+3=9x equation:

x2+3=9x

We move all terms to the left:

x2+3-(9x)=0

We add all the numbers together, and all the variables

x^2-9x+3=0

a = 1; b = -9; c = +3;
Δ = b2-4ac
Δ = -92-4·1·3
Δ = 69
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{69}}{2*1}=\frac{9-\sqrt{69}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{69}}{2*1}=\frac{9+\sqrt{69}}{2}
$