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-3x^2+224=-6x+2
We move all terms to the left:
-3x^2+224-(-6x+2)=0
We get rid of parentheses
-3x^2+6x-2+224=0
We add all the numbers together, and all the variables
-3x^2+6x+222=0
a = -3; b = 6; c = +222;
Δ = b2-4ac
Δ = 62-4·(-3)·222
Δ = 2700
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2700}=\sqrt{900*3}=\sqrt{900}*\sqrt{3}=30\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-30\sqrt{3}}{2*-3}=\frac{-6-30\sqrt{3}}{-6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+30\sqrt{3}}{2*-3}=\frac{-6+30\sqrt{3}}{-6} $
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