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108=16+3x^2
We move all terms to the left:
108-(16+3x^2)=0
We get rid of parentheses
-3x^2-16+108=0
We add all the numbers together, and all the variables
-3x^2+92=0
a = -3; b = 0; c = +92;
Δ = b2-4ac
Δ = 02-4·(-3)·92
Δ = 1104
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1104}=\sqrt{16*69}=\sqrt{16}*\sqrt{69}=4\sqrt{69}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{69}}{2*-3}=\frac{0-4\sqrt{69}}{-6} =-\frac{4\sqrt{69}}{-6} =-\frac{2\sqrt{69}}{-3} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{69}}{2*-3}=\frac{0+4\sqrt{69}}{-6} =\frac{4\sqrt{69}}{-6} =\frac{2\sqrt{69}}{-3} $
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