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2x^2-18=643
We move all terms to the left:
2x^2-18-(643)=0
We add all the numbers together, and all the variables
2x^2-661=0
a = 2; b = 0; c = -661;
Δ = b2-4ac
Δ = 02-4·2·(-661)
Δ = 5288
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5288}=\sqrt{4*1322}=\sqrt{4}*\sqrt{1322}=2\sqrt{1322}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{1322}}{2*2}=\frac{0-2\sqrt{1322}}{4} =-\frac{2\sqrt{1322}}{4} =-\frac{\sqrt{1322}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{1322}}{2*2}=\frac{0+2\sqrt{1322}}{4} =\frac{2\sqrt{1322}}{4} =\frac{\sqrt{1322}}{2} $
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