3x2+3x=8x+2

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Solution for 3x2+3x=8x+2 equation:



3x^2+3x=8x+2
We move all terms to the left:
3x^2+3x-(8x+2)=0
We get rid of parentheses
3x^2+3x-8x-2=0
We add all the numbers together, and all the variables
3x^2-5x-2=0
a = 3; b = -5; c = -2;
Δ = b2-4ac
Δ = -52-4·3·(-2)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-7}{2*3}=\frac{-2}{6} =-1/3 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+7}{2*3}=\frac{12}{6} =2 $

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