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3(x2-2)+3=46
We move all terms to the left:
3(x2-2)+3-(46)=0
We add all the numbers together, and all the variables
3(+x^2-2)+3-46=0
We add all the numbers together, and all the variables
3(+x^2-2)-43=0
We multiply parentheses
3x^2-6-43=0
We add all the numbers together, and all the variables
3x^2-49=0
a = 3; b = 0; c = -49;
Δ = b2-4ac
Δ = 02-4·3·(-49)
Δ = 588
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{588}=\sqrt{196*3}=\sqrt{196}*\sqrt{3}=14\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{3}}{2*3}=\frac{0-14\sqrt{3}}{6} =-\frac{14\sqrt{3}}{6} =-\frac{7\sqrt{3}}{3} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{3}}{2*3}=\frac{0+14\sqrt{3}}{6} =\frac{14\sqrt{3}}{6} =\frac{7\sqrt{3}}{3} $
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