# 3x^2-5x+1=8x^2-2x-9

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## Solution for 3x^2-5x+1=8x^2-2x-9 equation:

3x^2-5x+1=8x^2-2x-9
We move all terms to the left:
3x^2-5x+1-(8x^2-2x-9)=0
We get rid of parentheses
3x^2-8x^2-5x+2x+9+1=0
We add all the numbers together, and all the variables
-5x^2-3x+10=0
a = -5; b = -3; c = +10;Δ = b2-4acΔ = -32-4·(-5)·10Δ = 209The 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{-(-3)-\sqrt{209}}{2*-5}=\frac{3-\sqrt{209}}{-10}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{209}}{2*-5}=\frac{3+\sqrt{209}}{-10}$

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