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x2=42
We move all terms to the left:
x2-(42)=0
We add all the numbers together, and all the variables
x^2-42=0
a = 1; b = 0; c = -42;
Δ = b2-4ac
Δ = 02-4·1·(-42)
Δ = 168
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{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{42}}{2*1}=\frac{0-2\sqrt{42}}{2} =-\frac{2\sqrt{42}}{2} =-\sqrt{42}x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{42}}{2*1}=\frac{0+2\sqrt{42}}{2} =\frac{2\sqrt{42}}{2} =\sqrt{42}
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