3x+2x2=5x2-6

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Solution for 3x+2x2=5x2-6 equation:



3x+2x^2=5x^2-6
We move all terms to the left:
3x+2x^2-(5x^2-6)=0
We get rid of parentheses
2x^2-5x^2+3x+6=0
We add all the numbers together, and all the variables
-3x^2+3x+6=0
a = -3; b = 3; c = +6;
Δ = b2-4ac
Δ = 32-4·(-3)·6
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-9}{2*-3}=\frac{-12}{-6} =+2 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+9}{2*-3}=\frac{6}{-6} =-1 $

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