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11x^2=8
We move all terms to the left:
11x^2-(8)=0
a = 11; b = 0; c = -8;
Δ = b2-4ac
Δ = 02-4·11·(-8)
Δ = 352
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{22}}{2*11}=\frac{0-4\sqrt{22}}{22} =-\frac{4\sqrt{22}}{22} =-\frac{2\sqrt{22}}{11} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{22}}{2*11}=\frac{0+4\sqrt{22}}{22} =\frac{4\sqrt{22}}{22} =\frac{2\sqrt{22}}{11} $
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