3x^2+5x=-2x+6

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



3x^2+5x=-2x+6
We move all terms to the left:
3x^2+5x-(-2x+6)=0
We get rid of parentheses
3x^2+5x+2x-6=0
We add all the numbers together, and all the variables
3x^2+7x-6=0
a = 3; b = 7; c = -6;
Δ = b2-4ac
Δ = 72-4·3·(-6)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-11}{2*3}=\frac{-18}{6} =-3 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+11}{2*3}=\frac{4}{6} =2/3 $

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