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2x^2+5=50
We move all terms to the left:
2x^2+5-(50)=0
We add all the numbers together, and all the variables
2x^2-45=0
a = 2; b = 0; c = -45;
Δ = b2-4ac
Δ = 02-4·2·(-45)
Δ = 360
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{10}}{2*2}=\frac{0-6\sqrt{10}}{4} =-\frac{6\sqrt{10}}{4} =-\frac{3\sqrt{10}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{10}}{2*2}=\frac{0+6\sqrt{10}}{4} =\frac{6\sqrt{10}}{4} =\frac{3\sqrt{10}}{2} $
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