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-3x^2-6x+21=6x
We move all terms to the left:
-3x^2-6x+21-(6x)=0
We add all the numbers together, and all the variables
-3x^2-12x+21=0
a = -3; b = -12; c = +21;
Δ = b2-4ac
Δ = -122-4·(-3)·21
Δ = 396
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{11}}{2*-3}=\frac{12-6\sqrt{11}}{-6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{11}}{2*-3}=\frac{12+6\sqrt{11}}{-6} $
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