15=6x^2+6x+3

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Solution for 15=6x^2+6x+3 equation:



15=6x^2+6x+3
We move all terms to the left:
15-(6x^2+6x+3)=0
We get rid of parentheses
-6x^2-6x-3+15=0
We add all the numbers together, and all the variables
-6x^2-6x+12=0
a = -6; b = -6; c = +12;
Δ = b2-4ac
Δ = -62-4·(-6)·12
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-18}{2*-6}=\frac{-12}{-12} =1 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+18}{2*-6}=\frac{24}{-12} =-2 $

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