3x2+5x-1=2x2+6x+5

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Solution for 3x2+5x-1=2x2+6x+5 equation:



3x^2+5x-1=2x^2+6x+5
We move all terms to the left:
3x^2+5x-1-(2x^2+6x+5)=0
We get rid of parentheses
3x^2-2x^2+5x-6x-5-1=0
We add all the numbers together, and all the variables
x^2-1x-6=0
a = 1; b = -1; c = -6;
Δ = b2-4ac
Δ = -12-4·1·(-6)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-5}{2*1}=\frac{-4}{2} =-2 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+5}{2*1}=\frac{6}{2} =3 $

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