# 11x=3x^2-9

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## Solution for 11x=3x^2-9 equation:

11x=3x^2-9
We move all terms to the left:
11x-(3x^2-9)=0
We get rid of parentheses
-3x^2+11x+9=0
a = -3; b = 11; c = +9;Δ = b2-4acΔ = 112-4·(-3)·9Δ = 229The delta value is higher than zero, so the equation has two solutionsWe 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{-(11)-\sqrt{229}}{2*-3}=\frac{-11-\sqrt{229}}{-6}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{229}}{2*-3}=\frac{-11+\sqrt{229}}{-6}$

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