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8x^2+6=306
We move all terms to the left:
8x^2+6-(306)=0
We add all the numbers together, and all the variables
8x^2-300=0
a = 8; b = 0; c = -300;
Δ = b2-4ac
Δ = 02-4·8·(-300)
Δ = 9600
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{9600}=\sqrt{1600*6}=\sqrt{1600}*\sqrt{6}=40\sqrt{6}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{6}}{2*8}=\frac{0-40\sqrt{6}}{16} =-\frac{40\sqrt{6}}{16} =-\frac{5\sqrt{6}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{6}}{2*8}=\frac{0+40\sqrt{6}}{16} =\frac{40\sqrt{6}}{16} =\frac{5\sqrt{6}}{2} $
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