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5x^2=52
We move all terms to the left:
5x^2-(52)=0
a = 5; b = 0; c = -52;
Δ = b2-4ac
Δ = 02-4·5·(-52)
Δ = 1040
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1040}=\sqrt{16*65}=\sqrt{16}*\sqrt{65}=4\sqrt{65}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{65}}{2*5}=\frac{0-4\sqrt{65}}{10} =-\frac{4\sqrt{65}}{10} =-\frac{2\sqrt{65}}{5} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{65}}{2*5}=\frac{0+4\sqrt{65}}{10} =\frac{4\sqrt{65}}{10} =\frac{2\sqrt{65}}{5} $
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