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x2/2+6=13
We move all terms to the left:
x2/2+6-(13)=0
We add all the numbers together, and all the variables
x2/2-7=0
We multiply all the terms by the denominator
x2-7*2=0
We add all the numbers together, and all the variables
x^2-14=0
a = 1; b = 0; c = -14;
Δ = b2-4ac
Δ = 02-4·1·(-14)
Δ = 56
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{14}}{2*1}=\frac{0-2\sqrt{14}}{2} =-\frac{2\sqrt{14}}{2} =-\sqrt{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{14}}{2*1}=\frac{0+2\sqrt{14}}{2} =\frac{2\sqrt{14}}{2} =\sqrt{14} $
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