X*X+9=341*y

Solution for X*X+9=341*y equation:

X*X+9=341X

We move all terms to the left:

X*X+9-(341X)=0

We add all the numbers together, and all the variables

-341X+X*X+9=0

Wy multiply elements

X^2-341X+9=0

a = 1; b = -341; c = +9;
Δ = b2-4ac
Δ = -3412-4·1·9
Δ = 116245
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{-(-341)-\sqrt{116245}}{2*1}=\frac{341-\sqrt{116245}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-341)+\sqrt{116245}}{2*1}=\frac{341+\sqrt{116245}}{2}
$