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213124=29e^2+291
We move all terms to the left:
213124-(29e^2+291)=0
We get rid of parentheses
-29e^2-291+213124=0
We add all the numbers together, and all the variables
-29e^2+212833=0
a = -29; b = 0; c = +212833;
Δ = b2-4ac
Δ = 02-4·(-29)·212833
Δ = 24688628
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{24688628}=\sqrt{4*6172157}=\sqrt{4}*\sqrt{6172157}=2\sqrt{6172157}$$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{6172157}}{2*-29}=\frac{0-2\sqrt{6172157}}{-58} =-\frac{2\sqrt{6172157}}{-58} =-\frac{\sqrt{6172157}}{-29} $$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{6172157}}{2*-29}=\frac{0+2\sqrt{6172157}}{-58} =\frac{2\sqrt{6172157}}{-58} =\frac{\sqrt{6172157}}{-29} $
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